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Natural numbers Factors Multiples Prime factors

Here you will learn about equivalent fractions including how to simplify fractions and how to find equivalent fractions.

Students will first learn about equivalent fractions as part of number and operations in fractions in elementary school.

Equivalent fractions are fractions that have the same value. They help us to compare fractions, list them in order from least to greatest and write in lowest terms.

For example, find an equivalent fraction to \cfrac{1}{2}

For example, find an equivalent fraction to \cfrac{2}{3}

Notice that the numerator and the denominator were both multiplied by the same common factor of 3.

For example, find an equivalent fraction to \cfrac{2}{5}

Notice that the numerator and denominator were multiplied by a common factor of 2.

\cfrac{2\times2}{5\times2}=\cfrac{4}{10} \cfrac{2}{5}=\cfrac{4}{10}

For example, find an equivalent fraction to \cfrac{5}{6}

Notice that the numerator and denominator were multiplied by the whole number 2.

\cfrac{5 \times 2}{6 \times 2}=\cfrac{10}{12} \cfrac{5}{6}=\cfrac{10}{12}

How does this relate to 4th grade math and 5th grade math?

In order determine if the given fractions are equivalent:

In order to find a missing denominator or numerator of equivalent fractions:

Use this quiz to check your grade 4 to 6 students’ understanding of fractions. 10+ questions with answers covering a range of 4th, 5th and 6th grade topics to identify areas of strength and support!

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Use this quiz to check your grade 4 to 6 students’ understanding of fractions. 10+ questions with answers covering a range of 4th, 5th and 6th grade topics to identify areas of strength and support!

DOWNLOAD FREE

Determine if the fractions represented by the fraction strip are equivalent.

The denominator of the first fraction is 4 with 3 equal shaded parts. \cfrac{3}{4}

The denominator of the second fraction is 8 with 6 equal shaded parts. \cfrac{6}{8}

2Using either multiplication or division, find the common factor that was multiplied or divided from the first fraction to the second fraction.

Using multiplication, the common factor is 2.

\cfrac{3\times 2}{4\times 2}=\cfrac{6}{8}

3Write the equivalent fractions.

\cfrac{3}{4}=\cfrac{6}{8}

Determine if the fractions represented by the area models are equivalent.

Compare the numerators and denominators of the given fractions.

The first circle is divided into 16 equal parts with 6 parts shaded. \cfrac{6}{16}

The second circle is divided into 8 equal parts with 3 parts shaded. \cfrac{3}{8}

Using either multiplication or division, find the common factor that was multiplied or divided from the first fraction to the second fraction.

Using division, the common factor is 2.

\cfrac{6\div 2}{16\div 2}=\cfrac{3}{8}

Write the equivalent fractions.

Which fraction is equivalent to \cfrac{12}{18}?

\cfrac{4}{7}, \; \cfrac{2}{3}, \; \cfrac{1}{6}

Find the common factor.

\cfrac{12}{18}

\cfrac{12}{18}=\cfrac{2}{3} \; The numerators and denominators do have the same common factor. ✔

\cfrac{12}{18}

Multiply or divide the numerator and denominator of one of the fractions by the common factor.

\cfrac{12\div 6}{18\div 6}=\cfrac{2}{3} \; The common factor is 6. Divide the numerator and denominator by 6.

Write the equivalent fraction.

Find the missing denominator.

\cfrac{3}{5}=\cfrac{15}{?}

Find the common factor.

The numerator for the first fraction is 3 and the numerator of the second fraction is 15. The first numerator was multiplied by a common factor of 5 to get the second numerator of 15.

\cfrac{3\times 5}{5\times ?}=\cfrac{15}{?}

Multiply or divide the numerator and denominator of one of the fractions by the common factor.

Multiply the numerator and denominator by the common factor 5.

\cfrac{3\times5}{5\times5}=\cfrac{15}{?}

Write the equivalent fractions.

Find the missing numerator.

\cfrac{?}{20}=\cfrac{3}{5}

Find the common factor.

The denominators of the given fractions are 20 and 5.

20 \div 5 = 4

So the common factor is 4.

Multiply the numerator of the second fraction by the common factor.

Write the equivalent fraction.

Find the missing numerator.

\cfrac{24}{63}=\cfrac{?}{21}

Find the common factor.

The denominators of the given fractions are 63 and 21.

63 \div 3 = 21

So the common factor is 3.

Multiply or divide the numerator and denominator of one of the fractions by the common factor.

Write the equivalent fraction.

1.

Using the area models, represent the shaded area as equivalent fractions.

The first circle is divided into 5 equal parts with 3 parts shaded. \cfrac{3}{5}

The second circle is divided into 15 equal parts with 9 parts shaded. \cfrac{9}{15}

The equivalent fractions are \cfrac{3}{5}=\cfrac{9}{15}.

2. Which equivalent statement is true?

Looking at the fraction strip the top row has two shaded parts which equals \cfrac{2}{8} and the second row has one shaded part which equals \cfrac{1}{4}.

The equivalent fractions are \cfrac{2}{8}=\cfrac{1}{4}.

The common factor is 2.

\cfrac{2\div 2}{8\div 2}=\cfrac{1}{4}

3. Which fraction is equivalent to \cfrac{63}{108}?

Compare the numerator and denominator of the given fraction to the numerators and denominators of the answer choices to find a common factor. The common factor is 9.

\cfrac{63\div 9}{108\div 9}=\cfrac{7}{12}

\cfrac{63}{108}=\cfrac{7}{12}

4. Find the missing numerator.

\cfrac{3}{4}=\cfrac{?}{24}

18 is the missing numerator.

5. Find the missing denominator.

\cfrac{6}{7}=\cfrac{24}{?}

28 is the missing denominator.

6. Find the missing denominator.

\cfrac{24}{?}=\cfrac{3}{13}

104 is the missing denominator.

Equivalent fractions and “fraction families” are used to help us add and subtract fractions with unlike denominators and find common denominators. Equivalent fractions also help us to write fractions in simplest form.

Yes, using number lines is a powerful tool with fractions. It helps build understanding when comparing fractions with different denominators, different numerators, and building number sense.

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