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Domain Number and Operations—Fractions
Grade 4
Cluster Understand decimal notation for fractions, and compare decimal fractions.
Standard Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100.<span class='footnote'>Students who can generate equivalent fractions can develop strategies for adding fractions with unlike denominators in general. But addition and subtraction with unlike denominators in general is not a requirement at this grade.</span> <span class='clarification'>For example, express $3/10$ as $30/100$, and add $3/10 + 4/100 = 34/100$.</span>
Task Expanded Fractions and Decimals

Expanded Fractions and Decimals


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Alignments to Content Standards: 4.NF.C.5 4.NF.C.6
Student View

Task

Complete the table.

Fraction Expanded Fraction Form Expanded Decimal Form Decimal
$43 \frac{65}{100}$ $40 + 3 + \frac{6}{10} + \frac{5}{100} $ $40 + 3 + 0.6 + 0.05$ $43.65$
$21 \frac{90}{100}$
$40 \frac{76}{100}$
$7 \frac{82}{100}$
$18 \frac{3}{100}$

IM Commentary

The purpose of this task is for students to show they understand the connection between fraction and decimal notation by writing the same numbers both ways. Comparing and contrasting the two solutions shown below shows why decimal notation can be confusing. The first solution shows the briefest way to represent each number, and the second solution makes all the zeros explicit.

Solutions

Solution: Supressing unnecessary zeros

Fraction Expanded Fraction Form Expanded Decimal Form Decimal
$43 \frac{65}{100}$ $40 + 3 + \frac{6}{10} + \frac{5}{100} $ $40 + 3 + 0.6 + 0.05$ $43.65$
$21 \frac{90}{100}$ $20 + 1 + \frac{9}{10} $ $20 + 1 + 0.9 $ $21.9$
$40 \frac{76}{100}$ $40 + \frac{7}{10} + \frac{6}{100} $ $40 + 0.7 + 0.06$ $40.76$
$7 \frac{82}{100}$ $7 + \frac{8}{10} + \frac{2}{100} $ $7 + 0.8 + 0.02$ $\hskip 6pt 7.82$
$18 \frac{3}{100}$ $10 + 8 + \frac{3}{100} $ $10 + 8 + 0.03$ $18.03$

Solution: Keeping all zeros

Fraction Expanded Fraction Form Expanded Decimal Form Decimal
$43 \frac{65}{100}$ $40 + 3 + \frac{6}{10} + \frac{5}{100} $ $40 + 3 + 0.6 + 0.05$ $43.65$
$21 \frac{90}{100}$ $20 + 1 + \frac{9}{10} + \frac{0}{100} $ $20 + 1 + 0.9 + 0.00$ $21.90$
$40 \frac{76}{100}$ $40 + 0 + \frac{7}{10} + \frac{6}{100} $ $40 + 0 + 0.7 + 0.06$ $40.76$
$7 \frac{82}{100}$ $\hskip 6pt 0 + 7 + \frac{8}{10} + \frac{2}{100} $ $\hskip 6pt 0 + 7 + 0.8 + 0.02$ $\hskip 6pt 7.82$
$18 \frac{3}{100}$ $10 + 8 + \frac{0}{10} + \frac{3}{100} $ $10 + 8 + 0.0 + 0.03$ $18.03$

Expanded Fractions and Decimals

Complete the table.

Fraction Expanded Fraction Form Expanded Decimal Form Decimal
$43 \frac{65}{100}$ $40 + 3 + \frac{6}{10} + \frac{5}{100} $ $40 + 3 + 0.6 + 0.05$ $43.65$
$21 \frac{90}{100}$
$40 \frac{76}{100}$
$7 \frac{82}{100}$
$18 \frac{3}{100}$
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