Decompose means to break a number or shape into smaller parts that together make the whole. You can decompose 8 into 5 + 3, decompose 347 into 300 + 40 + 7, or decompose 34 into 14 + 24. Most numbers can be decomposed in many ways, and the parts always add back to the original.
Decomposing splits a whole into parts that add back to it: a number into smaller numbers, a number into place values, or a fraction into smaller fractions.
Formal definition and notation
To decompose a quantity n is to write it as a sum (or, for factoring, a product) of smaller quantities, n = a + b + ⋯, without changing its value. The reverse process, putting parts together, is called composing. Decomposing by place value gives expanded form; decomposing a fractionab gives a sum of fractions with denominatorb; decomposing a shape splits its area into simpler pieces.
Expanded form is one particular decomposition, by place value. 47 = 40 + 7 is expanded form; 47 = 30 + 17 is a decomposition but not expanded form.
Quick check: 3 questions
Question 1 of 3
Which is NOT a way to decompose 10?
Show answer and explanation
Answer: D. 8 + 3 = 11, not 10, so it does not decompose 10. The other three pairs all add to 10.
Question 2 of 3
Which decomposition of 4,062 uses place value correctly?
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Answer: B. 4 thousands, 0 hundreds, 6 tens and 2 ones: 4,000 + 60 + 2. Choice A shifts the 6 into the hundreds, C shrinks the 4 to hundreds, and D adds only the digits.
Question 3 of 3
Which sum is equal to 58?
Show answer and explanation
Answer: A.28 + 38 = 58: same eighths, numerators add to 5. The others change the denominator or add up to more than 58.
Decompose: frequently asked questions
What does decompose mean in kindergarten math?
It means breaking a small number into two parts in different ways and recording them. For 5, children find 4 and 1, 3 and 2, and so on, using fingers, cubes or drawings, and write equations such as 5 = 3 + 2. This builds the number sense behind making ten and later mental math.
What is the difference between compose and decompose?
They are opposites. Composing puts parts together to make a whole: 4 tens and 3 ones compose 43. Decomposing breaks the whole into parts: 43 decomposes into 40 + 3, or 30 + 13. Students switch between the two all the time, for example when they regroup in addition and subtraction.
How do you decompose a fraction?
Keep the denominator and split the numerator into parts that add to it. For 56 you could write 26 + 36 or 16 + 46. A mixed number can be decomposed into a whole and a fraction too: 213 = 1 + 1 + 13.
FactoringFactoring rewrites a number or expression as a product of factors. It is the reverse of multiplying or distributing: 12 = 3 × 4, 6x + 9 = 3(2x + 3) and x2 + 5x + 6 = (x + 2)(x + 3). Factoring changes the form, not the value, so multiplying the factors back gives the original.Algebra · Grade 6, Grade 7, Grade 8Place ValuePlace value is the value of a digit based on its position in a number. In 3,507 the 5 is worth 500, because it sits in the hundreds place. Each place is worth 10 times the place to its right: ones, tens, hundreds, thousands, and after the decimal point, tenths and hundredths.Number System · Grade 3, Grade 4, Grade 5Expanded FormExpanded form is a way of writing a number as the sum of the values of its digits. Each digit is multiplied by its place value, so 4072 = 4000 + 70 + 2, or 4 × 1000 + 7 × 10 + 2 × 1. It shows what every digit is worth. Zeros add nothing, so they are usually left out.Number System · Grade 2, Grade 3, Grade 4FractionA fraction is a number that names equal parts of a whole, written ab. The bottom number, the denominator, tells how many equal parts make one whole; the top number, the numerator, tells how many of those parts you have. So 34 means 3 of 4 equal parts. Every fraction is also a point on the number line.Number System · Grade 3, Grade 4, Grade 5DenominatorThe denominator is the bottom number in a fraction. It tells how many equal parts make one whole: in 35, the 5 means the whole is cut into 5 equal parts, and the numerator 3 counts the parts you have. The denominator can never be 0.Number System · Grade 3, Grade 4, Grade 5AreaArea is the amount of surface a flat shape covers, measured in square units. It counts how many unit squares fit inside the shape, which is why the units are squared. A rectangle’s area is length times width, so a 5 by 3 rectangle has area 15 square units.Geometry · Grade 3, Grade 4, Grade 5NumberA number is an amount or value used to count, measure, order and compare. We write numbers with digits (7), words (seven) or other symbols, but the number itself is the amount: 7 dots, the word seven and the numeral 7 all show the same number. Numbers include whole numbers, fractions, decimals and negatives.Number System · Kindergarten, Grade 1, Grade 2CircleA circle is the set of all points in a flat plane that are the same distance from one fixed point, the center. That distance is the radius. A segment through the center from edge to edge is the diameter, twice the radius. The distance around is the circumference, 2π r, and the area inside is π r2.Geometry · Kindergarten, Grade 1, Grade 7Whole NumberA whole number is 0 or a positive counting number: 0, 1, 2, 3, and so on. Whole numbers do not include fractions, decimals, or negative numbers, so 12 is a whole number but 8.5, 34 and −3 are not. Every whole number is also an integer.Number System · Grade 3, Grade 4, Grade 5Unit FractionA unit fraction is a fraction with a numerator of 1, such as 12, 15 or 112. It names one equal part of a whole split into that many parts. The bigger the denominator, the smaller the unit fraction, and every fraction ab is a copies of 1b.Number System · Grade 3, Grade 4, Grade 5SubtractionSubtraction is the operation that finds how much is left when you take one amount away from another, or how far apart two numbers are. It is written with a minus sign: 9 − 4 = 5. The answer is called the difference. Subtraction undoes addition, so you can check 9 − 4 = 5 by adding 5 + 4 = 9.Operations · Grade 1, Grade 2, Grade 3RegroupingRegrouping is trading 10 of one place value for 1 of the next larger place, or 1 for 10 of the next smaller place, so that column addition or subtraction works. In 47 + 38, the 15 ones become 1 ten and 5 ones; in 52 − 27, 1 ten becomes 10 ones. It is also called carrying and borrowing.Operations · Grade 1, Grade 2, Grade 3NumeratorThe numerator is the top number in a fraction. It tells how many parts are being counted, while the denominator below the fraction bar tells how many equal parts make one whole. In 35, the numerator is 3: three of five equal parts are taken.Number System · Grade 3, Grade 4, Grade 5FactorA factor is a number or expression that divides another number or expression evenly, with no remainder. Factors multiply together to make a product: 4 × 6 = 24, so 4 and 6 are factors of 24. Every whole number greater than 1 has at least two factors, 1 and itself.Number System · Grade 4, Grade 5, Grade 6AdditionAddition is the operation that puts amounts together to find the total. The numbers you add are called addends, the answer is the sum, and the sign is the plus sign, +. For example, 7 + 5 = 12. On a number line, adding a positive number means moving to the right.Operations · Kindergarten, Grade 1, Grade 2Mixed NumberA mixed number has a whole number and a fraction together, such as 234, which means 2 + 34. It represents a value greater than one whole when the whole-number part is positive. Every mixed number can be rewritten as an improper fraction, and back: 234 = 114.Number System · Grade 4, Grade 5, Grade 6Distributive PropertyThe distributive property says that multiplying a number by a sum gives the same result as multiplying it by each term and then adding: a(b + c) = ab + ac. It multiplies a factor by each term inside parentheses, so 3(x + 4) = 3x + 12. It works with subtraction too, and using it backward is factoring.Algebra · Grade 6, Grade 7, Grade 8Area ModelAn area model is a rectangle used to multiply or divide, with each side broken into place-value parts. To find 23 × 14, split the sides into 20 + 3 and 10 + 4, find the area of each smaller box (200, 30, 80, 12) and add these partial products: 322.Operations · Grade 3, Grade 4, Grade 5