Exercises on Equivalent Fractions

To the fractions that represent the same portion of a whole are called equivalent fractions. These fractions are obtained when we multiply or divide the numerator and denominator of a fraction by the same number.

Using equivalent fractions, we can simplification of fractions, Or the adding and subtracting fractions with different denominators. Thus, finding equivalent fractions is an essential procedure in calculations with fractional numbers.

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To learn more about this topic, check out a list of exercises solved on equivalent fractions.

List of exercises on equivalent fractions

Question 1. The fractions below are equivalent. Enter the number by which we multiply or divide the terms in the left fraction to arrive at the right fraction.

The) $\dpi{120} \frac{2}{9} \frac{6}{27}$

B) $\dpi{120} \frac{3}{10} \frac{21}{70}$

w) $\dpi{120} \frac{8}{4} \frac{2}{1}$

Question 2. Check that the fractions are equivalent by indicating the number by which the left fraction is multiplied or divided.

The) $\dpi{120} \frac{5}{8} \: e\: \frac{15}{24}$

B) $\dpi{120} \frac{3}{10} \: e\: \frac{12}{50}$

w) $\dpi{120} \frac{9}{45} \: e\: \frac{1}{5}$

Question 3. Check that the fractions are equivalent by cross-multiplying them.

The) $\dpi{120} \frac{3}{5} \: e\: \frac{15}{25}$

B) $\dpi{120} \frac{4}{6} \: e\: \frac{6}{9}$

w) $\dpi{120} \frac{1}{4} \: e\: \frac{3}{8}$

Question 4. What should be the value of $\dpi{120} x$ for the fractions below to be equivalent?

$\dpi{120} \frac{5}{9} \frac{x}{36}$

Question 5. Write a fraction with a denominator equal to 20 that is equivalent to each of the following fractions:

$\dpi{120} \frac{1}{2}\: \: \: \frac{3}{4} \: \: \: \frac{1}{5}$

Question 6. What is the equivalent fraction of $\dpi{120} \frac{6}{8}$ which has the number 54 as the numerator?

Question 7. Find a fraction equivalent to $\dpi{120} \frac{12}{36}$ that has the smallest possible terms.

Question 8. Determine the values of $\dpi{120} a, b \: \mathrm{e}\: c$ so that we have:

$\dpi{120} \frac{48}{72} \frac{24}{a} \frac{b}{18} \frac{6}{c} \frac{2}{3}$

Resolution of question 1

Since fractions are equivalent, to find such a number, simply divide the larger numerator by the smaller numerator or the larger denominator by the smaller denominator.

The) $\dpi{120} \frac{2}{9} \frac{6}{27}$

As 6: 2 = 3 and 27: 9 = 3, then the number is 3.

B) $\dpi{120} \frac{3}{10} \frac{21}{70}$

As 21: 3 = 7 and 70: 10 = 10, then the number is 7.

w) $\dpi{120} \frac{8}{4} \frac{2}{1}$

Since 8: 2 = 4 and 4: 1 = 4, then the number is 4.

Resolution of question 2

For fractions to be equivalent, dividing the larger numerator by the smaller numerator and dividing the larger denominator by the smaller denominator must have the same result.

The) $\dpi{120} \frac{5}{8} \: e\: \frac{15}{24}$

15: 5 = 3 and 24: 8 = 3

We get the same number, so they're equivalent fractions.

The fraction on the left must be multiplied by 3 to get the fraction on the right.

B) $\dpi{120} \frac{3}{10} \: e\: \frac{12}{50}$

12: 3 = 4 and 50: 10 = 5

We get different numbers, so the fractions are not equivalent.

w) $\dpi{120} \frac{9}{45} \: e\: \frac{1}{5}$

9: 1 = 9 and 45: 5 = 9

We get the same number, so they're equivalent fractions.

The fraction on the left must be divided by 9 to get the fraction on the right.

Resolution of question 3

The) $\dpi{120} \frac{3}{5} \: e\: \frac{15}{25}$

Doing the cross multiplication:

3. 25 = 75

15. 5 = 75

We get the same number, so they're equivalent.

B) $\dpi{120} \frac{4}{6} \: e\: \frac{6}{9}$

4. 9 = 36

6. 6 = 36

We get the same number, so they're equivalent.

w) $\dpi{120} \frac{1}{4} \: e\: \frac{3}{8}$

1. 8 = 8

3. 4 = 12

We get different numbers, so they are not equivalent.

Resolution of question 4

$\dpi{120} \frac{5}{9} \frac{x}{36}$

As 36: 9 = 4, then, for the fractions to be equivalent, we must have $\dpi{120} x: 5 4$ . What is the number $\dpi{120} x$ for this to happen?

$\dpi{120} x 20$ , because 20: 5 = 4

Thus, we have the following equivalent fractions:

$\dpi{120} \frac{5}{9} \frac{20}{36}$

Resolution of question 5

We already know that the denominator is 20, what we need to figure out is the numerator of each fraction. In each case, let's call this number $\dpi{120} x$ .

First fraction:

$\dpi{120} \frac{1}{2} \frac{x}{20}$ As 20: 2 = 10, then we must have $\dpi{120} x: 1 10$ . What is the value of $\dpi{120} x$ for this to happen?

$\dpi{120} x 10$ → $\dpi{120} \mathbf{\frac{1}{2} \frac{10}{20}}$

Next fraction: $\dpi{120} \frac{3}{4} \frac{x}{20}$

Since 20: 4 = 5, then we must have x: 3 = 5. What is the value of x for this to happen?

x = 15 → $\dpi{120} \mathbf{\frac{3}{4} \frac{15}{20}}$

Last fraction:

$\dpi{120} \frac{1}{5} \frac{x}{20}$

Since 20: 5 = 4, then we must have x: 1 = 4. What is the value of x for this to happen?

x = 4 → $\dpi{120} \mathbf{\frac{1}{5} \frac{4}{20}}$

Resolution of question 6

Let's call x the denominator of the fraction with numerator equal to 54.

$\dpi{120} \frac{6}{8} \frac{54}{x}$

Since 54: 6 = 9, then we must have x: 8 = 9. What is the number x for this to happen?

x = 72, because 72: 8 = 9

So we have the equivalent fractions:

$\dpi{120} \frac{6}{8} \frac{54}{72}$

Resolution of question 7

To find an equivalent fraction with the smallest possible terms, we must divide the terms by the same number until this is no longer possible.

We can divide by 2:

$\dpi{120} \frac{12}{36} \frac{6}{18}$

Now, we can divide the obtained fraction by 2, as well:

$\dpi{120} \frac{12}{36} \frac{6}{18} \frac{3}{9}$

Dividing the last fraction by 3:

$\dpi{120} \frac{12}{36} \frac{6}{18} \frac{3}{9} \frac{1}{3}$

We can't divide the terms of the fraction $\dpi{120} \frac{1}{3}$ by the same number. This means that this is the equivalent fraction of $\dpi{120} \frac{12}{36}$ with the lowest possible terms.