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Subtract Mixed Numbers with Like Denominators

Students subtract mixed numbers with like denominators, including cases requiring regrouping from the whole number part when the fractional part being subtracted is larger than the fractional part of the minuend.

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Subtract Mixed Numbers with Like Denominators

Grade 4 · Adding and Subtracting Mixed Numbers · question 1 of 3

0 of 20

20 rungs. A star at the top.

7 − 1 1/5 =

How it is taught

0:00 of 3:25

Like denominators let you subtract the fraction parts as they are.

If the top fraction is too small, regroup one whole into that denominator.

Read it: Whole bars and pieces

1 2/3 + 1 2/3: the pieces come to 4/3, so 3 of them make 1 more whole bar, and the sum is 3 1/3. Taking away, a whole bar opens into 3 pieces when the pieces are too few.

  1. Work with the pieces first: put them together, or take them away.
  2. Pieces that make 3/3 become 1 more whole bar; too few pieces open 1 whole bar.
  3. Then the whole bars, and count what you have: wholes, then pieces.

3/3 is 1 whole, so 3 pieces of 1/3 are as much as a whole bar.

The fraction part of a mixed number is less than 1 whole, so 4/3 still holds a whole bar.

Opening a whole bar into 3 pieces does not change how much there is, only how it is cut.

Add or take away the pieces, then the whole bars, making or opening a whole bar when the pieces need it.

Leaving the pieces as 4/3 and writing 2 4/3.

4/3 is more than 1 whole: 3/3 of it is 1 more whole bar. So 1 2/3 + 1 2/3 is 3 1/3.

5 2/4 − 1 3/4 = ___ — 3 3/4. 2 pieces are not enough to take 3 away, so 1 whole opens into 4 pieces: 3 3/4.

4 1/4 − 1 3/4

Let's subtract mixed numbers. We have four and one-fourth pizzas, and we eat one and three-fourths. How much is left?

Write the problem in column form: four and one-fourth minus one and three-fourths.

Look at the fractions. One-fourth is smaller than three-fourths, so we can't subtract yet.

414 − 134 = ?Eat 134 — how much remains?414−13414 < 34Borrow 1 whole31 = 4444 + 14 = 545424212ANSWER212pizzas left
Grade 4 · Regrouping a whole into fourths

We need to regroup. Borrow one whole from the four.

Four becomes three, because we took one whole away.

That one whole is the same as four-fourths. Add it to the one-fourth we already had.

Now the top number is three and five-fourths.

Subtract the fractions: five-fourths minus three-fourths is two-fourths.

Subtract the wholes: three minus one is two.

Two-fourths simplifies to one-half.

So four and one-fourth minus one and three-fourths is two and one-half. Great work!

What you see

While they climb, your page writes one true line to ask about tonight, and a short note each Sunday.

MayaGrade 3 · Mathematics
Did you know?

A chessboard has 64 squares — share them out between the 8 rows and each row holds exactly 8.

Today’s goal
1 star — one skill mastered, every rung of its ladder climbed
Climbing now
Divide within 100

An example student.

MayaGrade 3 · Mathematics

Maya earned 2 stars this week — Interpret multiplication as equal groups, which took 6 answers over 3 days before its star landed 3 days ago and Multiply by 6, 7, 8 and 9. Next up: Divide within 100.

An example week.

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