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Multiplication•Grade 5•Vertical Format

Grade 5 Multiplication Vertical Format

Grade 5 multiplication vertical format sheet: 16 problems on three-digit by two-digit multiplication, two-digit by two-digit multiplication, four-digit by one-digit multiplication.

CCSSAligned to Common Core 5.NBT.5: Fluently multiply multi-digit whole numbers using the standard algorithm.

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Three different problem sets — same skill, same layout, fresh numbers.

Preview — Set A

Solve each problem. Line up the place values and show any regrouping.

  1. 1.
    135
    ×89
  2. 2.
    55
    ×59
  3. 3.
    9948
    ×2
  4. 4.
    536
    ×72
  5. 5.
    69
    ×20
  6. 6.
    8187
    ×3
  7. 7.
    482
    ×48
  8. 8.
    30
    ×58
  9. 9.
    4726
    ×4
  10. 10.
    411
    ×59
  11. 11.
    90
    ×65
  12. 12.
    7277
    ×7
  13. 13.
    613
    ×32
  14. 14.
    89
    ×55
  15. 15.
    2436
    ×3
  16. 16.
    980
    ×28

Other ways to solve this

Using 135 × 89 from this sheet (Set A, problem 1). Each method below reaches the same answer, 12,015, by a different route; pick the one that makes the most sense to you.

Partial products

Helps you see every piece of a long multiplication before adding them up.

135
× 89
459 × 5
2709 × 30
9009 × 100
40080 × 5
2,40080 × 30
8,00080 × 100
12,015

  1. Step 1Split 135 into 100 + 30 + 5 and 89 into 80 + 9.

  2. Step 2Multiply each part of 89 by each part of 135, starting with the ones.

    • 9 × 5 = 45
    • 9 × 30 = 270
    • 9 × 100 = 900
    • 80 × 5 = 400
    • 80 × 30 = 2,400
    • 80 × 100 = 8,000

  3. Step 3Add the partial products: 45 + 270 + 900 + 400 + 2,400 + 8,000 = 12,015.

  4. Step 4So 135 × 89 = 12,015.

Step 1 of 4

Lattice method

Helps keep carrying tidy: every digit product gets its own box, and you only add at the end.

Lattice for 135 × 89A 3 by 2 lattice with 135 across the top and 89 down the right side. Each box holds a digit product split by a diagonal, and the diagonal sums are written down the left side and along the bottom.1358908244009274512015

  1. Step 1Write 135 across the top and 89 down the right side, one digit per box.

  2. Step 2Multiply each pair of digits. Put the tens above the diagonal and the ones below it.

    • 8 × 1 = 8 → tens 0, ones 8
    • 8 × 3 = 24 → tens 2, ones 4
    • 8 × 5 = 40 → tens 4, ones 0
    • 9 × 1 = 9 → tens 0, ones 9
    • 9 × 3 = 27 → tens 2, ones 7
    • 9 × 5 = 45 → tens 4, ones 5

  3. Step 3Add along each diagonal, starting at the bottom right. Carry when a sum is 10 or more.

    • Diagonal 1 (from the bottom right): 5 = 5
    • Diagonal 2 (from the bottom right): 11 = 11: write 1, carry 1
    • Diagonal 3 (from the bottom right): 19 + carry 1 = 20: write 0, carry 2
    • Diagonal 4 (from the bottom right): 10 + carry 2 = 12: write 2, carry 1
    • Diagonal 5 (from the bottom right): 0 + carry 1 = 1

  4. Step 4Read the digits down the left side and along the bottom: 1 2 0 1 5. So 135 × 89 = 12,015.

Step 1 of 4

Doubling and halving

Helps when you can halve and double quickly: the only hard step is one addition at the end.

Halving the left column and doubling the right. Rows with an even left value are crossed out.
HalveDoubleKeep?
89135keep
44270cross out
22540cross out
111,080keep
52,160keep
24,320cross out
18,640keep

  1. Step 1Put the smaller number, 89, in the left column and 135 in the right column.

  2. Step 2Halve the left number (drop any remainder) and double the right number, row by row, until the left reaches 1.

    • 89 | 135
    • 44 | 270
    • 22 | 540
    • 11 | 1,080
    • 5 | 2,160
    • 2 | 4,320
    • 1 | 8,640

  3. Step 3Cross out every row with an even number on the left.

    • Cross out 44 | 270
    • Cross out 22 | 540
    • Cross out 2 | 4,320

  4. Step 4Add the right column of the rows that are left: 135 + 1,080 + 2,160 + 8,640 = 12,015.

  5. Step 5So 135 × 89 = 12,015.

Step 1 of 5

What this worksheet covers

Set A of this grade 5 vertical format sheet holds sixteen multiplication problems on one printable page, with the answer key on the page behind it. The numbers run as high as 9,948. Two problems from the middle of the page — "8187 × 3" and "90 × 65" — show the range. Common Core 5.NBT.5 is the slot this page fills.

Skills practiced

The grade 5 multiplication sequence covers three-digit by two-digit multiplication and multiplying by powers of ten; this page sits inside it. What a student is asked to do here is three-digit by two-digit multiplication, two-digit by two-digit multiplication, and four-digit by one-digit multiplication. Concretely, the sheet tests whether a student can recall the multiplication facts quickly and accurately, without counting up to them.

About the vertical format format

The 16 problems here — problem 6, "8187 × 3", for one — are printed in column form, the layout the standard algorithm is written for. Stacked factors put the partial products in columns, which is where the place-value shift in long multiplication lives.

Set A, Set B and Set C

The three sets come from the same generator with three different seeds: same skill, same layout, fresh numbers, and an answer key computed with the problems. Where Set A's problem 9 is "4726 × 4", Set B's is "8419 × 4".

How to use this worksheet

Work the sixteen problems straight through, then check against the key together rather than handing it back marked; asking a grade 5 student to find their own multiplication error teaches more than seeing it circled. Date the vertical format before filing it. Set C from six weeks later is the cheapest evidence you have that the multiplication stuck.

One mistake to watch for

In two-digit multiplication the second partial product is not shifted left, so 34 × 12 is answered 102 instead of 408. Problem 4 on this grade 5 vertical format page, "536 × 72", is where to look for it.

The 1 in 12 is being treated as one, not ten.

Have the student write the placeholder zero in the ones column of the second row and say "ten times" aloud as they start it.

The full guide to teaching multiplicationTeaching multiplication from equal groups to integer exponents: the grade 2–8 progression, times-table strategies, and the errors that stall students.

Other grade 5 multiplication formats

The same skill in the other formats available at this grade.

A step either side

The same format one grade down and one grade up — the easier sheet is often the faster fix when this one is not landing.

Vertical Format sheets in other grade 5 topics

Free to download, print and photocopy for a whole class: three vertical format sheets of grade 5 multiplication, sixteen problems each, keys included.

← All grade 5 multiplication worksheetsMultiplication, every gradeGrade 5 mathBuild your own in the generatorCommon Core 5.NBT.5

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