Testinar Grade 3 math

Equivalent Fractions as Same Size

Students will recognize equivalent fractions as the same size or the same point on a number line.

CH04-02 Fractions

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Score: ____ / 8

Directions Solve each problem. Show your reasoning on the page or on separate paper. Check the answer key only after finishing.

Two fraction bars are shown. Bar 1 shows \(\frac{2}{3}\) shaded. Bar 2 shows \(\frac{4}{6}\) shaded. The shaded regions are the same size. Which statement is true?
1. \(\frac{2}{3}<\frac{4}{6}\)
2. \(\frac{2}{3}>\frac{4}{6}\)
3. \(\frac{2}{3}=\frac{4}{6}\)
4. Cannot be compared
Look at the two circles. Circle A shows \(\frac{1}{2}\) shaded. Circle B shows \(\frac{2}{4}\) shaded. Both circles are the same size. What can you say about these fractions?
1. They are not related
2. \(\frac{1}{2}<\frac{2}{4}\)
3. \(\frac{1}{2}>\frac{2}{4}\)
4. \(\frac{1}{2}=\frac{2}{4}\)
Ben draws two bars. Bar 1 is divided into 4 equal parts with 2 parts shaded. Bar 2 is divided into 8 equal parts with 4 parts shaded. The bars are the same length. Are the shaded regions the same size?
1. No, Bar 1 is larger.
2. Cannot tell without measuring.
3. No, Bar 2 is larger.
4. Yes, they are the same size.
Which pair of fractions shows the SAME amount shaded?
1. \(\frac{1}{2}\) and \(\frac{2}{4}\)
2. \(\frac{2}{4}\) and \(\frac{2}{8}\)
3. \(\frac{1}{2}\) and \(\frac{2}{8}\)
4. \(\frac{2}{4}\) and \(\frac{3}{8}\)
Ava has two ribbons. Both ribbons are the same length. She colors \(\frac{3}{6}\) of one ribbon red and \(\frac{1}{2}\) of the other ribbon red. Does she color the same amount on both ribbons?
1. It depends on the ribbon length.
2. No, the first ribbon has more.
3. Yes, both are the same.
4. No, the second ribbon has more.
Look at the rectangle. It is divided into 6 equal parts, and 2 parts are shaded. Which other fraction is EQUAL to the shaded amount?
1. \(\frac{3}{8}\)
2. \(\frac{1}{3}\)
3. \(\frac{2}{8}\)
4. \(\frac{1}{4}\)
Two pies are the same size. Pie A is cut into 4 slices and 3 are eaten. Pie B is cut into 8 slices and 6 are eaten. How much pie is left in each case?
1. Cannot tell without tasting.
2. The same amount left.
3. Pie B has more left.
4. Pie A has more left.
Sam has two chocolate bars. Bar 1 is split into 3 equal pieces. Bar 2 is split into 6 equal pieces. He eats \(\frac{2}{6}\) of Bar 2. What fraction of Bar 1 equals what he ate?
1. \(\frac{2}{3}\)
2. \(\frac{1}{6}\)
3. \(\frac{3}{6}\)
4. \(\frac{1}{3}\)

Teacher and parent reference

Answer key and explanations

C. \(\frac{2}{3}=\frac{4}{6}\)
Two fractions are equivalent if they represent the same-size region. Since both shaded regions are equal, \(\frac{2}{3}=\frac{4}{6}\).
D. \(\frac{1}{2}=\frac{2}{4}\)
Both circles show the same shaded area. \(\frac{1}{2}\) of one circle equals \(\frac{2}{4}\) of another equal-sized circle. They are equivalent.
D. Yes, they are the same size.
\(\frac{2}{4}\) and \(\frac{4}{8}\) are equivalent because both show one-half of the bar shaded. When denominator doubles, the numerator also doubles to maintain the same-size region.
A. \(\frac{1}{2}\) and \(\frac{2}{4}\)
Both bars show the same shaded region (one-half of each bar). They are equivalent fractions.
C. Yes, both are the same.
\(\frac{3}{6}=\frac{1}{2}\) because both represent one-half of the ribbon.
B. \(\frac{1}{3}\)
\(\frac{2}{6}=\frac{1}{3}\) because both represent one-third of the rectangle.
B. The same amount left.
Pie A has \(\frac{1}{4}\) left. Pie B has \(\frac{2}{8}\) left. These are equivalent: \(\frac{1}{4}=\frac{2}{8}\).
D. \(\frac{1}{3}\)
\(\frac{2}{6}=\frac{1}{3}\). When Sam eats \(\frac{2}{6}\) of Bar 2, he ate the same amount as \(\frac{1}{3}\) of Bar 1.