The big ideaTake away the tens and the ones, row by row. Each row works on its own.
How it works
Put the first number on the frame. Take away by sliding beads back, the tens row and the ones row each on its own.
Start with the tens: the tens row is the big place. Read the rows that are still across.
The ones row never touches the tens row, because each row works alone.
When nothing needs to be borrowed, tens first or ones first gives the same answer.
What is left, 62: six tens and two ones.
Example 1: Tens, then ones
Put 86 on the frame: eight tens and six ones.
Slide 2 tens back: 8 - 2 = 6 tens.
Slide 4 ones back: 6 - 4 = 2 ones.
86 - 24 = 62
6 tens and 2 ones are left: 62.
Example 2: Take away a smaller number
Put 62 on the frame.
Slide back 3 tens: 6 - 3 = 3 tens.
Slide back 1 one: 2 - 1 = 1 one.
62 - 31 = 31
3 tens and 1 one are left: 31.
Example 3: Nothing to take from the ones
Take away exactly 20, which is two tens and no ones.
The ones row stays still, and only the tens row slides back: 6 - 2 = 4 tens.
62 - 20 = 42
The 2 ones stay: 42.
Example 4: A sum that needs a new trick
Look at 72 - 28. The ones row has only 2 beads.
Two cannot give away eight.
That needs borrowing, which comes next.
Words to know
take away
Slide beads back to the left.
tens row
The top row on a two-row frame. Each bead is worth ten.
ones row
The bottom row. Each bead is worth one.
borrowing
A new trick for when a row has too few beads.
Watch out
Take away from each row on its own: tens from tens, ones from ones.
Beads slid back are gone. Read the beads that are still across.
Look at each ones digit first. If it is too small, you need to borrow.
Try it
What is 78 - 35?
What is 96 - 52?
What is 85 - 30?
Does 72 - 28 need a new trick?
Answers: 1. 43 · 2. 44 · 3. 55 · 4. yes
Try at homeAsk a grown-up to pick a two-digit number and a smaller one, like seventy-eight and thirty-five, with every digit of the second no bigger than the digit above it. Take away the tens, then the ones, and check on paper or with a calculator.
For grown-upsPick two numbers like 78 and 35, where each digit of the second is no bigger than the digit above it, and check the answer with a calculator.
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