Number and Operations—Fractions: Understanding Fractions as Sums of Unit Fractions (CCSS.4.NF.3)
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Common Core 4th Grade Math › Number and Operations—Fractions: Understanding Fractions as Sums of Unit Fractions (CCSS.4.NF.3)
What is the sum? $\frac{2}{8} + \frac{3}{8}$
$\frac{5}{16}$
$\frac{5}{8}$
$\frac{2}{11}$
$1\ \frac{5}{8}$
Explanation
Think of a fraction bar split into 8 equal parts. Shade 2 parts on one bar and 3 parts on another. When you combine them, 5 parts out of 8 are shaded, so the sum is $\frac{5}{8}$. The incorrect choice $\frac{5}{16}$ comes from adding denominators, which you should not do when denominators are the same.
Which shows $\frac{7}{8}$ written as $\frac{5}{8} + \frac{2}{8}$?
$\frac{7}{8} = \frac{5}{8} + \frac{2}{8}$
$\frac{7}{8} = \frac{5}{8} + \frac{3}{8}$
$\frac{7}{8} = \frac{5}{16} + \frac{2}{16}$
$\frac{7}{8} = \frac{5}{8} + \frac{2}{16}$
Explanation
Picture a circle divided into 8 equal slices. Shade 7 slices. You can think of that as one group of 5 shaded slices and another group of 2 shaded slices. Together they make 7 out of 8, so $\frac{7}{8} = \frac{5}{8} + \frac{2}{8}$.
What is the sum? $2\frac{3}{8} + 1\frac{4}{8}$
$4\ \frac{7}{16}$
$2\ \frac{7}{16}$
$3\ \frac{7}{8}$
$4\ \frac{7}{8}$
Explanation
Use fraction bars: two whole bars and a bar with $\frac{3}{8}$, plus one whole bar and a bar with $\frac{4}{8}$. Combine wholes: $2 + 1 = 3$. Combine parts: $\frac{3}{8} + \frac{4}{8} = \frac{7}{8}$. Total is $3\ \frac{7}{8}$. Do not add denominators; that error leads to seventeenths or sixteenths.