3rd Grade Equivalent and Comparing Fractions Worksheet Solutions (PDF)

3rd Grade math worksheet solutions: Equivalent and Comparing Fractions – Maths PDF

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This grade 3 equivalent fractions answers for 3rd Grade covers equivalent and comparing fractions (Common Core 3.NF.A.3), with a free PDF to print.

Each answer explains the model or rule that gives the result. For comparisons, check that the symbol opens toward the greater fraction. Models and number lines in the answers match the ones on the worksheet.

Grade 3 · Common Core State Standards: 3.NF.A.3

Grade 3 equivalent fractions answers: exercises 1 to 10

Exercise 1 – Halves and fourths

The shaded part of the fourths bar is 2 parts of 4. It matches the halves bar.

Answer: \(\frac{2}{4}\)

Exercise 2 – Thirds and sixths

Each third is cut into 2 sixths, so one third is 2 sixths.

Answer: \(\frac{2}{6}\)

Exercise 3 – Sixths and halves on lines

The dashed line passes through the middle mark of the halves line.

The point 3/6 is also 1/2.

Answer: \(\frac{1}{2}\)

Exercise 4 – Fill the blank

Each fourth is 2 eighths, so 3 fourths are 6 eighths.

Answer: \(\frac{6}{8}\)

Exercise 5 – Equal to one half

Half of 4 parts is 2, half of 6 is 3, and half of 8 is 4.

Answer: \(\frac{2}{4}\), \(\frac{3}{6}\), \(\frac{4}{8}\)

Exercise 6 – Missing numerators

\(\frac{1}{4} = \frac{2}{8}\)
\(\frac{4}{8} = \frac{1}{2}\)
\(\frac{4}{6} = \frac{2}{3}\)

Exercise 7 – Fractions equal to a whole

Exercise 8 – Whole number on the line

P is 4 halves from 0.

P is the same point as 2.

Answer: \(\frac{4}{2}\) = 2

Exercise 9 – Whole numbers as fractions

\(\frac{3}{1}\)
\(\frac{8}{4}\)
\(\frac{6}{6}\)

Exercise 10 – Same denominator

\(\frac{3}{8} < \frac{5}{8}\)
\(\frac{6}{6} > \frac{4}{6}\)
\(\frac{1}{3} < \frac{2}{3}\)

Exercises 11 and up

Exercise 11 – Same numerator with bars

The fourths bar has more shaded length.

The top shaded part is longer.

Answer: \(\frac{3}{4} > \frac{3}{8}\)

Exercise 12 – Same numerator

\(\frac{2}{3} > \frac{2}{6}\)
\(\frac{5}{8} < \frac{5}{6}\)
\(\frac{1}{2} > \frac{1}{4}\)

Exercise 13 – Which point is greater

B is farther right than A.

Answer: B; \(\frac{4}{6} > \frac{1}{6}\)

Exercise 14 – Order the fractions

All numerators are 1, so bigger denominators mean smaller parts.

Answer: \(\frac{1}{8}\), \(\frac{1}{6}\), \(\frac{1}{3}\), \(\frac{1}{2}\)

Exercise 15 – Banana loaves

Maya ate \(\frac{6}{8}\) and Sofia ate \(\frac{3}{4}\). Both shaded lengths are equal, so the fractions are equivalent.

Answer: Yes, \(\frac{6}{8}\) = \(\frac{3}{4}\)

Exercise 16 – Who ran farther

The numerators match. Fourths are bigger than eighths.

Answer: Liam; \(\frac{3}{4} > \frac{3}{8}\)

Exercise 17 – Painted boards

Jamal, because 5 sixths is greater than 3 sixths.
5 – 3 = 2, so \(\frac{2}{6}\) more.

Exercise 18 – Noah's rule

The denominator tells how many equal parts the whole has. More parts means each part is smaller, so fourths are smaller than thirds.

Answer: \(\frac{1}{4} < \frac{1}{3}\)

Exercise 19 – Scoops of rice

Priya: 9 thirds, and every 3 thirds make 1 cup, so \(\frac{9}{3}\) = 3 cups. Diego: 12 fourths, and every 4 fourths make 1 cup, so \(\frac{12}{4}\) = 3 cups.

Answer: Neither. Both poured 3 cups.

Exercise 20 – Ribbon contest

Diego, because \(\frac{3}{6}\) = \(\frac{1}{2}\).
\(\frac{2}{3} = \frac{4}{6}\), so the order is \(\frac{3}{6}\), \(\frac{2}{3}\), \(\frac{5}{6}\) (Diego, Priya, Mei).

Key facts behind this grade 3 equivalent fractions answers

Key facts

Equivalent fractions name the same amount and sit at the same point on a number line.
Examples with denominators 2, 3, 4, 6, and 8: 1/2 = 2/4 = 4/8 and 2/3 = 4/6.
A fraction with the same top and bottom number equals 1, and n/1 equals n.
Same denominator: the greater numerator makes the greater fraction.
Same numerator: the smaller denominator makes the greater fraction.

How to use this grade 3 equivalent fractions answers

Cover each solution, solve the exercise again, then uncover it and compare every line. If your answer differs, find the first step that changed and redo the exercise from there.

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