Add and Subtract Fractions with Common Denominators

Model Fraction Addition

How many quarters are pictured? One quarter plus \(2\) quarters equals \(3\) quarters.

Remember, quarters are really fractions of a dollar. Quarters are another way to say fourths. So the picture of the coins shows that

\[\begin{array}{lllll}\frac{1}{4} & & \frac{2}{4} & & \frac{3}{4} \\ \text{one quarter} & + & \text{two quarters} & = & \text{three quarters}\end{array}\]

Let’s use fraction circles to model the same example, \(\frac{1}{4}+\frac{2}{4}.\)

Start with one \(\frac{1}{4}\) piece.
Add two more \(\frac{1}{4}\)pieces.
The result is \(\frac{3}{4}\).

So again, we see that

\[\frac{1}{4}+\frac{2}{4}=\frac{3}{4}\]

Example

Try it.

Use a model to find the sum \(\frac{3}{8}+\frac{2}{8}.\)

Solution

Start with three \(\frac{1}{8}\) pieces.
Add two \(\frac{1}{8}\)pieces.
How many \(\frac{1}{8}\)pieces are there?

There are five \(\frac{1}{8}\) pieces, or five-eighths. The model shows that \(\frac{3}{8}+\frac{2}{8}=\frac{5}{8}.\)

Add Fractions with a Common Denominator

shows that to add the same-size pieces, meaning that the fractions have the same denominator, we just add the number of pieces.

Example

Try it.

Find the sum: \(\frac{3}{5}+\frac{1}{5}.\)

Solution

	\(\frac{3}{5}+\frac{1}{5}\)
Add the numerators and place the sum over the common denominator.	\(\frac{3+1}{5}\)
Simplify.	\(\frac{4}{5}\)

Example

Try it.

Find the sum: \(\frac{x}{3}+\frac{2}{3}.\)

Solution

	\(\frac{x}{3}+\frac{2}{3}\)
Add the numerators and place the sum over the common denominator.	\(\frac{x+2}{3}\)

Note that we cannot simplify this fraction any more. Since \(x\) and \(2\) are not like terms, we cannot combine them.

Example

Try it.

Find the sum: \(-\frac{9}{d}+\frac{3}{d}.\)

Solution

We will begin by rewriting the first fraction with the negative sign in the numerator.

\(-\frac{a}{b}=\frac{-a}{b}\)

	\(-\frac{9}{d}+\frac{3}{d}\)
Rewrite the first fraction with the negative in the numerator.	\(\frac{-9}{d}+\frac{3}{d}\)
Add the numerators and place the sum over the common denominator.	\(\frac{-9+3}{d}\)
Simplify the numerator.	\(\frac{-6}{d}\)
Rewrite with negative sign in front of the fraction.	\(-\frac{6}{d}\)

Example

Try it.

Find the sum: \(\frac{2n}{11}+\frac{5n}{11}.\)

Solution

	\(\frac{2n}{11}+\frac{5n}{11}\)
Add the numerators and place the sum over the common denominator.	\(\frac{2n+5n}{11}\)
Combine like terms.	\(\frac{7n}{11}\)

Example

Try it.

Find the sum: \(-\frac{3}{12}+(-\frac{5}{12}).\)

Solution

	\(-\frac{3}{12}+(-\frac{5}{12})\)
Add the numerators and place the sum over the common denominator.	\(\frac{-3+(-5)}{12}\)
Add.	\(\frac{-8}{12}\)
Simplify the fraction.	\(-\frac{2}{3}\)

Model Fraction Subtraction

Subtracting two fractions with common denominators is much like adding fractions. Think of a pizza that was cut into \(12\) slices. Suppose five pieces are eaten for dinner. This means that, after dinner, there are seven pieces (or \(\frac{7}{12}\) of the pizza) left in the box. If Leonardo eats \(2\) of these remaining pieces (or \(\frac{2}{12}\) of the pizza), how much is left? There would be \(5\) pieces left (or \(\frac{5}{12}\) of the pizza).

\[\frac{7}{12}-\frac{2}{12}=\frac{5}{12}\]

Let’s use fraction circles to model the same example, \(\frac{7}{12}-\frac{2}{12}.\)

Start with seven \(\frac{1}{12}\) pieces. Take away two \(\frac{1}{12}\) pieces. How many twelfths are left?

Again, we have five twelfths, \(\frac{5}{12}.\)

Example

Try it.

Use fraction circles to find the difference: \(\frac{4}{5}-\frac{1}{5}.\)

Solution

Start with four \(\frac{1}{5}\) pieces. Take away one \(\frac{1}{5}\) piece. Count how many fifths are left. There are three \(\frac{1}{5}\) pieces left.

Subtract Fractions with a Common Denominator

We subtract fractions with a common denominator in much the same way as we add fractions with a common denominator.

Example

Try it.

Find the difference: \(\frac{23}{24}-\frac{14}{24}.\)

Solution

	\(\frac{23}{24}-\frac{14}{24}\)
Subtract the numerators and place the difference over the common denominator.	\(\frac{23-14}{24}\)
Simplify the numerator.	\(\frac{9}{24}\)
Simplify the fraction by removing common factors.	\(\frac{3}{8}\)

Example

Try it.

Find the difference: \(\frac{y}{6}-\frac{1}{6}.\)

Solution

	\(\frac{y}{6}-\frac{1}{6}\)
Subtract the numerators and place the difference over the common denominator.	\(\frac{y-1}{6}\)

The fraction is simplified because we cannot combine the terms in the numerator.

Example

Try it.

Find the difference: \(-\frac{10}{x}-\frac{4}{x}.\)

Solution

Remember, the fraction \(-\frac{10}{x}\) can be written as \(\frac{-10}{x}.\)

	\(-\frac{10}{x}-\frac{4}{x}\)
Subtract the numerators.	\(\frac{-10-4}{x}\)
Simplify.	\(\frac{-14}{x}\)
Rewrite with the negative sign in front of the fraction.	\(-\frac{14}{x}\)

Now lets do an example that involves both addition and subtraction.

Example

Try it.

Simplify: \(\frac{3}{8}+(-\frac{5}{8})-\frac{1}{8}.\)

Solution

	\(\frac{3}{8}+(-\frac{5}{8})-\frac{1}{8}\)
Combine the numerators over the common denominator.	\(\frac{3+(-5)-1}{8}\)
Simplify the numerator, working left to right.	\(\frac{-2-1}{8}\)
Subtract the terms in the numerator.	\(\frac{-3}{8}\)
Rewrite with the negative sign in front of the fraction.	\(-\frac{3}{8}\)

Key Concepts

• Fraction Addition
  • If \(a,b,\) and \(c\) are numbers where \(c\ne 0\), then \(\frac{a}{c}+\frac{b}{c}=\frac{a+b}{c}\).
  • To add fractions, add the numerators and place the sum over the common denominator.
• Fraction Subtraction
  • If \(a,b,\) and \(c\) are numbers where \(c\ne 0\), then \(\frac{a}{c}-\frac{b}{c}=\frac{a-b}{c}\).
  • To subtract fractions, subtract the numerators and place the difference over the common denominator.

Add and Subtract Fractions with Common Denominators

Model Fraction Addition

In the following exercises, use a model to add the fractions. Show a diagram to illustrate your model.

Try it.

\(\frac{2}{5}+\frac{1}{5}\)

Try it.

\(\frac{3}{10}+\frac{4}{10}\)

Solution

\(\frac{7}{10}\)

Try it.

\(\frac{1}{6}+\frac{3}{6}\)

Try it.

\(\frac{3}{8}+\frac{3}{8}\)

Solution

\(\frac{3}{4}\)

Add Fractions with a Common Denominator

In the following exercises, find each sum.

Try it.

\(\frac{4}{9}+\frac{1}{9}\)

Try it.

\(\frac{2}{9}+\frac{5}{9}\)

Solution

\(\frac{7}{9}\)

Try it.

\(\frac{6}{13}+\frac{7}{13}\)

Try it.

\(\frac{9}{15}+\frac{7}{15}\)

Solution

\(\frac{16}{15}\)

Try it.

\(\frac{x}{4}+\frac{3}{4}\)

Try it.

\(\frac{y}{3}+\frac{2}{3}\)

Solution

\(\frac{y+2}{3}\)

Try it.

\(\frac{7}{p}+\frac{9}{p}\)

Try it.

\(\frac{8}{q}+\frac{6}{q}\)

Solution

\(\frac{14}{q}\)

Try it.

\(\frac{8b}{9}+\frac{3b}{9}\)

Try it.

\(\frac{5a}{7}+\frac{4a}{7}\)

Solution

\(\frac{9a}{7}\)

Try it.

\(\frac{-12y}{8}+\frac{3y}{8}\)

Try it.

\(\frac{-11x}{5}+\frac{7x}{5}\)

Solution

\(\frac{-4x}{5}\)

Try it.

\(-\frac{1}{8}+(-\frac{3}{8})\)

Try it.

\(-\frac{1}{8}+(-\frac{5}{8})\)

Solution

\(-\frac{3}{4}\)

Try it.

\(-\frac{3}{16}+(-\frac{7}{16})\)

Try it.

\(-\frac{5}{16}+(-\frac{9}{16})\)

Solution

\(-\frac{7}{8}\)

Try it.

\(-\frac{8}{17}+\frac{15}{17}\)

Try it.

\(-\frac{9}{19}+\frac{17}{19}\)

Solution

\(\frac{8}{19}\)

Try it.

\(\frac{6}{13}+(-\frac{10}{13})+(-\frac{12}{13})\)

Try it.

\(\frac{5}{12}+(-\frac{7}{12})+(-\frac{11}{12})\)

Solution

\(-\frac{13}{12}\)

Model Fraction Subtraction

In the following exercises, use a model to subtract the fractions. Show a diagram to illustrate your model.

Try it.

\(\frac{5}{8}-\frac{2}{8}\)

Try it.

\(\frac{5}{6}-\frac{2}{6}\)

Solution

\(\frac{1}{2}\)

Subtract Fractions with a Common Denominator

In the following exercises, find the difference.

Try it.

\(\frac{4}{5}-\frac{1}{5}\)

Try it.

\(\frac{4}{5}-\frac{3}{5}\)

Solution

\(\frac{1}{5}\)

Try it.

\(\frac{11}{15}-\frac{7}{15}\)

Try it.

\(\frac{9}{13}-\frac{4}{13}\)

Solution

\(\frac{5}{13}\)

Try it.

\(\frac{11}{12}-\frac{5}{12}\)

Try it.

\(\frac{7}{12}-\frac{5}{12}\)

Solution

\(\frac{1}{6}\)

Try it.

\(\frac{4}{21}-\frac{19}{21}\)

Try it.

\(-\frac{8}{9}-\frac{16}{9}\)

Solution

\(-\frac{8}{3}\)

Try it.

\(\frac{y}{17}-\frac{9}{17}\)

Try it.

\(\frac{x}{19}-\frac{8}{19}\)

Solution

\(\frac{x-8}{19}\)

Try it.

\(\frac{5y}{8}-\frac{7}{8}\)

Try it.

\(\frac{11z}{13}-\frac{8}{13}\)

Solution

\(\frac{11z-8}{13}\)

Try it.

\(-\frac{8}{d}-\frac{3}{d}\)

Try it.

\(-\frac{7}{c}-\frac{7}{c}\)

Solution

\(-\frac{14}{c}\)

Try it.

\(-\frac{23}{u}-\frac{15}{u}\)

Try it.

\(-\frac{29}{v}-\frac{26}{v}\)

Solution

\(-\frac{55}{v}\)

Try it.

\(\frac{6c}{7}-\frac{5c}{7}\)

Try it.

\(\frac{12d}{11}-\frac{9d}{11}\)

Solution

\(\frac{3d}{11}\)

Try it.

\(\frac{-4r}{13}-\frac{5r}{13}\)

Try it.

\(\frac{-7s}{3}-\frac{7s}{3}\)

Solution

\(-\frac{14s}{3}\)

Try it.

\(-\frac{3}{5}-(-\frac{4}{5})\)

Try it.

\(-\frac{3}{7}-(-\frac{5}{7})\)

Solution

\(\frac{2}{7}\)

Try it.

\(-\frac{7}{9}-(-\frac{5}{9})\)

Try it.

\(-\frac{8}{11}-(-\frac{5}{11})\)

Solution

\(-\frac{3}{11}\)

Mixed Practice

In the following exercises, perform the indicated operation and write your answers in simplified form.

Try it.

\(-\frac{5}{18}\cdot \frac{9}{10}\)

Try it.

\(-\frac{3}{14}\cdot \frac{7}{12}\)

Solution

\(-\frac{1}{8}\)

Try it.

\(\frac{n}{5}-\frac{4}{5}\)

Try it.

\(\frac{6}{11}-\frac{s}{11}\)

Solution

\(\frac{6-s}{11}\)

Try it.

\(-\frac{7}{24}+\frac{2}{24}\)

Try it.

\(-\frac{5}{18}+\frac{1}{18}\)

Solution

\(-\frac{2}{9}\)

Try it.

\(\frac{8}{15}\div \frac{12}{5}\)

Try it.

\(\frac{7}{12}\div \frac{9}{28}\)

Solution

\(\frac{49}{27}\)

Condensed: the full section is in OpenStax Prealgebra 2e.

Tani ti. Asnjë kalkulator nuk e zgjidh këtë, por pjesët e saj janë të llogaritura. Provo një më poshtë, ose shkruaj tënde.

⌨ Lloji ✎ E vizatova.

Problemi yt matematikor.

π Zgjidh

Praktiko (40)

Provo secilin në letër së pari. Zbulo përgjigjen për të kontrolluar; ato të verifikuara mund të hapen në zgjidhës për çdo hap.

1. Simplify: \(2x+9+3x-4.\)

   Puno mbi të. Pjesmarrës

   Zbulo përgjigjen

   \(5x+5\)

2. Draw a model of the fraction \(\frac{3}{4}.\)

   Puno mbi të. Pjesmarrës

3. Simplify: \(\frac{3+2}{6}.\)

   Puno mbi të. Pjesmarrës

   Zbulo përgjigjen

   \(\frac{5}{6}\)

4. Use a model to find the sum \(\frac{3}{8}+\frac{2}{8}.\)

   Puno mbi të. Pjesmarrës

   Zbulo përgjigjen

   Start with three \(\frac{1}{8}\) pieces.
   Add two \(\frac{1}{8}\)pieces.
   How many \(\frac{1}{8}\)pieces are there?

   There are five \(\frac{1}{8}\) pieces, or five-eighths. The model shows that \(\frac{3}{8}+\frac{2}{8}=\frac{5}{8}.\)

5. Use a model to find each sum. Show a diagram to illustrate your model.

   \(\frac{1}{8}+\frac{4}{8}\)

   Puno mbi të. Pjesmarrës

   Zbulo përgjigjen

   \(\frac{5}{8}\)

6. Use a model to find each sum. Show a diagram to illustrate your model.

   \(\frac{1}{6}+\frac{4}{6}\)

   Puno mbi të. Pjesmarrës

   Zbulo përgjigjen

   \(\frac{5}{6}\)

7. Find the sum: \(\frac{3}{5}+\frac{1}{5}.\)

   Puno mbi të. Pjesmarrës

   Zbulo përgjigjen

   	\(\frac{3}{5}+\frac{1}{5}\)
   Add the numerators and place the sum over the common denominator.	\(\frac{3+1}{5}\)
   Simplify.	\(\frac{4}{5}\)

8. Find each sum: \(\frac{3}{6}+\frac{2}{6}.\)

   Puno mbi të. Pjesmarrës

   Zbulo përgjigjen

   \(\frac{5}{6}\)

9. Find each sum: \(\frac{3}{10}+\frac{7}{10}.\)

   Puno mbi të. Pjesmarrës

   Zbulo përgjigjen

   1

10. Find the sum: \(\frac{x}{3}+\frac{2}{3}.\)

    Puno mbi të. Pjesmarrës

    Zbulo përgjigjen

    	\(\frac{x}{3}+\frac{2}{3}\)
    Add the numerators and place the sum over the common denominator.	\(\frac{x+2}{3}\)

    Note that we cannot simplify this fraction any more. Since \(x\) and \(2\) are not like terms, we cannot combine them.

11. Find the sum: \(\frac{x}{4}+\frac{3}{4}.\)

    Puno mbi të. Pjesmarrës

    Zbulo përgjigjen

    \(\frac{x+3}{4}\)

12. Find the sum: \(\frac{y}{8}+\frac{5}{8}.\)

    Puno mbi të. Pjesmarrës

    Zbulo përgjigjen

    \(\frac{y+5}{8}\)

13. Find the sum: \(-\frac{9}{d}+\frac{3}{d}.\)

    Puno mbi të. Pjesmarrës

    Zbulo përgjigjen

    We will begin by rewriting the first fraction with the negative sign in the numerator.

    \(-\frac{a}{b}=\frac{-a}{b}\)

    	\(-\frac{9}{d}+\frac{3}{d}\)
    Rewrite the first fraction with the negative in the numerator.	\(\frac{-9}{d}+\frac{3}{d}\)
    Add the numerators and place the sum over the common denominator.	\(\frac{-9+3}{d}\)
    Simplify the numerator.	\(\frac{-6}{d}\)
    Rewrite with negative sign in front of the fraction.	\(-\frac{6}{d}\)

14. Find the sum: \(-\frac{7}{d}+\frac{8}{d}.\)

    Puno mbi të. Pjesmarrës

    Zbulo përgjigjen

    \(\frac{1}{d}\)

15. Find the sum: \(-\frac{6}{m}+\frac{9}{m}.\)

    Puno mbi të. Pjesmarrës

    Zbulo përgjigjen

    \(\frac{3}{m}\)

16. Find the sum: \(\frac{2n}{11}+\frac{5n}{11}.\)

    Puno mbi të. Pjesmarrës

    Zbulo përgjigjen

    	\(\frac{2n}{11}+\frac{5n}{11}\)
    Add the numerators and place the sum over the common denominator.	\(\frac{2n+5n}{11}\)
    Combine like terms.	\(\frac{7n}{11}\)

17. Find the sum: \(\frac{3p}{8}+\frac{6p}{8}.\)

    Puno mbi të. Pjesmarrës

    Zbulo përgjigjen

    \(\frac{9p}{8}\)

18. Find the sum: \(\frac{2q}{5}+\frac{7q}{5}.\)

    Puno mbi të. Pjesmarrës

    Zbulo përgjigjen

    \(\frac{9q}{5}\)

19. Find the sum: \(-\frac{3}{12}+(-\frac{5}{12}).\)

    Puno mbi të. Pjesmarrës

    Zbulo përgjigjen

    	\(-\frac{3}{12}+(-\frac{5}{12})\)
    Add the numerators and place the sum over the common denominator.	\(\frac{-3+(-5)}{12}\)
    Add.	\(\frac{-8}{12}\)
    Simplify the fraction.	\(-\frac{2}{3}\)

20. Find each sum: \(-\frac{4}{15}+(-\frac{6}{15}).\)

    Puno mbi të. Pjesmarrës

    Zbulo përgjigjen

    \(-\frac{2}{3}\)

21. Find each sum: \(-\frac{5}{21}+(-\frac{9}{21}).\)

    Puno mbi të. Pjesmarrës

    Zbulo përgjigjen

    \(-\frac{2}{3}\)

22. Use fraction circles to find the difference: \(\frac{4}{5}-\frac{1}{5}.\)

    Puno mbi të. Pjesmarrës

    Zbulo përgjigjen

    Start with four \(\frac{1}{5}\) pieces. Take away one \(\frac{1}{5}\) piece. Count how many fifths are left. There are three \(\frac{1}{5}\) pieces left.

23. Use a model to find each difference. Show a diagram to illustrate your model.

    \(\frac{7}{8}-\frac{4}{8}\)

    Puno mbi të. Pjesmarrës

    Zbulo përgjigjen

    \(\frac{3}{8}\), models may differ.

24. Use a model to find each difference. Show a diagram to illustrate your model.

    \(\frac{5}{6}-\frac{4}{6}\)

    Puno mbi të. Pjesmarrës

    Zbulo përgjigjen

    \(\frac{1}{6}\), models may differ

25. Find the difference: \(\frac{23}{24}-\frac{14}{24}.\)

    Puno mbi të. Pjesmarrës

    Zbulo përgjigjen

    	\(\frac{23}{24}-\frac{14}{24}\)
    Subtract the numerators and place the difference over the common denominator.	\(\frac{23-14}{24}\)
    Simplify the numerator.	\(\frac{9}{24}\)
    Simplify the fraction by removing common factors.	\(\frac{3}{8}\)

26. Find the difference: \(\frac{19}{28}-\frac{7}{28}.\)

    Puno mbi të. Pjesmarrës

    Zbulo përgjigjen

    \(\frac{3}{7}\)

27. Find the difference: \(\frac{27}{32}-\frac{11}{32}.\)

    Puno mbi të. Pjesmarrës

    Zbulo përgjigjen

    \(\frac{1}{2}\)

28. Find the difference: \(\frac{y}{6}-\frac{1}{6}.\)

    Puno mbi të. Pjesmarrës

    Zbulo përgjigjen

    	\(\frac{y}{6}-\frac{1}{6}\)
    Subtract the numerators and place the difference over the common denominator.	\(\frac{y-1}{6}\)

    The fraction is simplified because we cannot combine the terms in the numerator.

29. Find the difference: \(\frac{x}{7}-\frac{2}{7}.\)

    Puno mbi të. Pjesmarrës

    Zbulo përgjigjen

    \(\frac{x-2}{7}\)

30. Find the difference: \(\frac{y}{14}-\frac{13}{14}.\)

    Puno mbi të. Pjesmarrës

    Zbulo përgjigjen

    \(\frac{y-13}{14}\)

31. Find the difference: \(-\frac{10}{x}-\frac{4}{x}.\)

    Puno mbi të. Pjesmarrës

    Zbulo përgjigjen

    Remember, the fraction \(-\frac{10}{x}\) can be written as \(\frac{-10}{x}.\)

    	\(-\frac{10}{x}-\frac{4}{x}\)
    Subtract the numerators.	\(\frac{-10-4}{x}\)
    Simplify.	\(\frac{-14}{x}\)
    Rewrite with the negative sign in front of the fraction.	\(-\frac{14}{x}\)

32. Find the difference: \(-\frac{9}{x}-\frac{7}{x}.\)

    Puno mbi të. Pjesmarrës

    Zbulo përgjigjen

    \(-\frac{16}{x}\)

33. Find the difference: \(-\frac{17}{a}-\frac{5}{a}.\)

    Puno mbi të. Pjesmarrës

    Zbulo përgjigjen

    \(-\frac{22}{a}\)

34. Simplify: \(\frac{3}{8}+(-\frac{5}{8})-\frac{1}{8}.\)

    Puno mbi të. Pjesmarrës

    Zbulo përgjigjen

    	\(\frac{3}{8}+(-\frac{5}{8})-\frac{1}{8}\)
    Combine the numerators over the common denominator.	\(\frac{3+(-5)-1}{8}\)
    Simplify the numerator, working left to right.	\(\frac{-2-1}{8}\)
    Subtract the terms in the numerator.	\(\frac{-3}{8}\)
    Rewrite with the negative sign in front of the fraction.	\(-\frac{3}{8}\)

35. Simplify: \(\frac{2}{5}+(-\frac{4}{5})-\frac{3}{5}.\)

    Puno mbi të. Pjesmarrës

    Zbulo përgjigjen

    −1

36. Simplify: \(\frac{5}{9}+(-\frac{4}{9})-\frac{7}{9}.\)

    Puno mbi të. Pjesmarrës

    Zbulo përgjigjen

    \(-\frac{2}{3}\)

37. \(\frac{2}{5}+\frac{1}{5}\)

    Puno mbi të. Pjesmarrës

38. \(\frac{3}{10}+\frac{4}{10}\)

    Puno mbi të. Pjesmarrës

    Zbulo përgjigjen

    \(\frac{7}{10}\)

39. \(\frac{1}{6}+\frac{3}{6}\)

    Puno mbi të. Pjesmarrës

40. \(\frac{3}{8}+\frac{3}{8}\)

    Puno mbi të. Pjesmarrës

    Zbulo përgjigjen

    \(\frac{3}{4}\)

Mbaje punën tënde

Një llogari e lirë shtohet shënime në çdo mësim, një regjistrim të asaj që ju keni përfunduar, problemet tuaja të zgjidhura në një vend, dhe një mësues që ju mund të pyesni rreth kësaj faqeje. Matematika vetë është e hapur për të gjithë, të regjistruar apo jo.

Regjistrohu Hyr

Simbolet e përdorura këtu

Prek çdo simbol për përkufizimin e plotë, një fotografi dhe se çfarë do të thotë çdo shkronjë në të.

\neqnot equal
The two sides are different.\pmplus or minus
Both signs at once: x = 3 ± 2 means 5 and 1.\leqless/greater than or equal
Inequalities that allow equality; < and > exclude it.\approxapproximately equal
Equal to the precision shown, not exactly.\sqrt{x}square root, n-th root
The non-negative number whose square (n-th power) is x.a \bmod nremainder
What is left after dividing a by n.\%per cent
Per hundred: 15% = 15/100.a : bratio, fraction
a for every b; a divided by b.

Si: Add and Subtract Fractions with Common Denominators

1. Model fraction addition
2. Add fractions with a common denominator
3. Model fraction subtraction
4. Subtract fractions with a common denominator
5. If
6. To add fractions, add the numerators and place the sum over the common denominator.
7. If
8. To subtract fractions, subtract the numerators and place the difference over the common denominator.

Pyetja që bëjnë njerëzit

Why does the order of operations matter?

Because 2 + 3 × 4 would otherwise be two different numbers. The convention (brackets, exponents, multiplication and division, addition and subtraction) exists so every reader gets the same value from the same expression.

How do I check an arithmetic answer?

Estimate first (round every number and compute roughly), then compare. If the estimate and the exact answer disagree by more than a little, one of them is wrong. The solver shows every operation, so you can find which line went astray.

Why are fractions harder than decimals?

They are not harder, they are more exact: 1/3 is a precise number, 0.333 is an approximation. Fractions need a common denominator to add, which is the one extra step people trip on.

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Më shumë në Arithmetic

Order of operationsFractionsPercentagesPowers and roots