Arithmetic glossary
The words arithmetic uses, in plain language, each one pointing at the rung where it is actually taught. If a word in a worked example or a question is unfamiliar, it is here.
29 terms
- Addend
- A number being added. In 7 + 5 = 12, both 7 and 5 are addends, and it makes no difference which is which.
- Rung 2: Addition
- Array
- Dots arranged in equal rows and columns. Five rows of four is an array holding twenty, and turning it sideways shows four rows of five is the same twenty.
- Rung 4: Multiplication
- Counting on
- Adding by continuing the count instead of starting again: to add three to eight, say nine, ten, eleven. It is the first way addition is ever done.
- Rung 2: Addition
- Decimal point
- The mark that separates wholes from parts of a whole. Everything left of the point is a whole number; each place to the right is a tenth, then a hundredth, then a thousandth.
- Rung 9: Decimals
- Denominator
- The number underneath a fraction. It names the size of the parts by saying how many equal parts the whole was cut into, so eighths have an 8 underneath because eight of them remake the whole.
- Rung 8: Fractions
- Difference
- The result of a subtraction, read as the gap between two numbers: the difference between 9 and 4 is 5, whether you count back from 9 or count on from 4.
- Rung 3: Subtraction
- Digit
- One of the ten symbols 0 to 9. A digit is a single mark; the number it stands for depends on the place it occupies.
- Rung 6: Place value
- Dividend
- The number being shared out. In 12 ÷ 3 = 4, the 12 is the dividend: twelve things, shared fairly.
- Rung 5: Division
- Divisor
- The number of groups, or the size of each group, in a division. In 12 ÷ 3 = 4, the 3 is the divisor.
- Rung 5: Division
- Equal parts
- Pieces of exactly the same size. Without them there is no fraction: a bar cut into one long piece and one short one has two pieces, but not two halves.
- Rung 8: Fractions
- Estimate
- A number close enough to be useful. Rounding to the nearest ten first turns 38 + 31 into 40 + 30, which is quick to do and close enough to check the real answer.
- Rung 7: Rounding
- Factor
- A number that divides another exactly, leaving nothing over. The factors of 12 are 1, 2, 3, 4, 6 and 12.
- Rung 4: Multiplication
- Hundredth
- One of a hundred equal parts of a whole, written 0.01 or 1/100. Ten hundredths make a tenth, and a hundred of them make the whole.
- Rung 9: Decimals
- Number bond
- Two numbers that make a given total, such as 7 and 3 making 10. Knowing the bonds to ten by heart is what makes carrying and borrowing quick.
- Rung 2: Addition
- Number line
- A line where every point is a number, with smaller numbers to the left and larger to the right. It is the same line whether you are counting, subtracting, rounding or going below zero.
- Rung 7: Rounding
- Numerator
- The number on top of a fraction. It counts how many of the equal parts you are talking about, so three shaded parts of four is 3/4.
- Rung 8: Fractions
- Percentage
- A fraction written out of a hundred, so the bottom number is always 100 and only the top is written. 42% means 42/100, which is 0.42.
- Rung 10: Percentages
- Place value
- What a digit is worth because of where it sits. The 3 in 34 is worth thirty and the 3 in 43 is worth three, because the same digit in a different column is a different amount.
- Rung 6: Place value
- Product
- The result of a multiplication. The product of 6 and 4 is 24, which can be read as six rows of four or four rows of six.
- Rung 4: Multiplication
- Quotient
- The result of a division when it divides exactly. In 35 ÷ 5 = 7, the 7 is the quotient.
- Rung 5: Division
- Ratio
- A comparison of two shares with each other rather than with the whole. A ratio of 4 : 8 means twelve parts split four and eight, and it simplifies to 1 : 2.
- Rung 12: Ratio
- Regrouping
- Moving ten ones into one ten, or breaking a ten back into ones, so a column can be worked. It is what makes carrying and borrowing possible.
- Rung 6: Place value
- Remainder
- What is left over when a number will not divide exactly. Thirteen shared between four gives three each with one remainder, because one cannot stretch to another round.
- Rung 5: Division
- Rounding
- Replacing a number with the nearest landmark. 38 rounds to 40 because 38 is closer to 40 than to 30; 35 rounds up by the halfway convention.
- Rung 7: Rounding
- Simplest form
- The same fraction written with the fewest, largest parts. 4/6 is the same amount as 2/3, and 2/3 is its simplest form.
- Rung 8: Fractions
- Take away
- The subtraction reading where counters are physically removed: twelve take away three leaves nine.
- Rung 3: Subtraction
- Tenth
- One of ten equal parts of a whole, written 0.1 or 1/10. Ten tenths make the whole, which is why the place after the point is worth a tenth.
- Rung 9: Decimals
- Whole number
- A number with nothing after the point: 0, 1, 2, 3 and on. Counting produces whole numbers, and fractions and decimals are what you get when a whole is not enough.
- Rung 1: Counting
Where these words are taught
Every term above belongs to one of the 12 rungs, taught in the order the ideas depend on each other.