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Number Trail Grade 4 / Week 07 / Tuesday
2/6
Week 07 · Equal and compare fractions

Tuesday

Multiply to find equal fractions
// Same amount, different parts
⏱ about 15 min

Tuesday: Multiply to find equal fractions

Riley spreads a puzzle on a flat stump. It is cut into 4 equal pieces.

"I have 3 of the 4 pieces," he says. "That is 3/4."

Then he cuts every piece into 2 smaller pieces.

"Now there are 8 pieces, and I have 6 of them."

Bennie nods. "You doubled the parts, so you doubled the pieces you have."

"The numerator and the denominator were both multiplied by 2."

"So 3/4 = 6/8," says Riley. "Same puzzle, smaller pieces!"

Learn it: multiply the top and bottom

Three bars the same length, showing three fourths, six eighths and nine twelfths shaded

Split each fourth into 2 parts: 3/4 = (3 × 2)/(4 × 2) = 6/8.

Split each fourth into 3 parts: 3/4 = (3 × 3)/(4 × 3) = 9/12.

Multiplying both numbers by the same number gives an equivalent fraction.

It works because each part is split the same way.

Multiply byFraction
2(1 × 2)/(2 × 2) = 2/4
3(1 × 3)/(2 × 3) = 3/6
4(1 × 4)/(2 × 4) = 4/8
5(1 × 5)/(2 × 5) = 5/10
6(1 × 6)/(2 × 6) = 6/12

All of these are equal to 1/2.

FIND THE MISSING NUMERATOR
  • Read the question.
  • Tap your answer.
3/4 = ?/12
2/5 = ?/10
5/6 = ?/12
3/10 = ?/100
GO BACK TO BIGGER PARTS
  • Read the question.
  • Tap your answer.
6/8 = ?/4
8/12 = ?/3
2/10 = ?/5
70/100 = ?/10
FIND THE MISSING DENOMINATOR
  • Read the question.
  • Tap your answer.
1/? = 4/12
5/? = 10/12
3/? = 6/10
4/? = 40/100

Learn it: tenths and hundredths

Multiply by 10 to turn tenths into hundredths.

3/10 = (3 × 10)/(10 × 10) = 30/100.

WHICH IS NOT EQUAL?
  • Read the question.
  • Tap your answer.
Which fraction is not equal to 2/5?
Which fraction is not equal to 1/4?
STEPS TO FIND A FRACTION EQUAL TO 2/3 IN TWELFTHS
  • Think about how Riley splits the parts.
  • Tap the steps in order.
1First
2Next
3Then
4Last
SentenceTrue or false?
3/4 = 9/12?
3/10 = 30/100?
2/3 = 3/4?
5/6 = 10/12?
WHY THIS EXERCISE2/3 is not 3/4. Adding 1 to both numbers does not make an equal fraction.
Try it
Fold a paper strip in fourths. Color 3 parts.
Now fold it in half again, the same way.
Count all the parts and the colored parts.
Write the two equal fractions you made.
Draw a bar for 2/5. Then split each part in two to show 4/10.

Same puzzle, smaller pieces! Tomorrow we compare fractions.

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