OST Grade 5 Math flashcards

32 cards. Read the term and the definition here. The deck at the top of this page is optional.

Decimal place value

Each place in a decimal is ten times the place to its right. In 6.482, the 4 means 4 tenths, the 8 means 8 hundredths, and the 2 means 2 thousandths.

Rounding decimals

Locate the place being rounded, then check the one digit to its right. If that digit is 5 or greater, increase the target digit by one; otherwise leave it. 5.738 rounded to hundredths is 5.74.

Comparing decimals

Compare digit by digit from the left, starting with whole numbers, then tenths, hundredths, and so on. The first place where digits differ decides the comparison; 0.7 is greater than 0.68.

Multiplying by powers of ten

Multiplying by 10, 100, or 1,000 moves every digit that many places to the left, so 0.45 × 100 = 45. Dividing moves digits right, so 32 ÷ 1,000 = 0.032.

Order of operations

Work through grouping symbols first, then multiplication and division from left to right, then addition and subtraction from left to right. For 8 + 3 × (10 − 6), the value is 20.

Numerical expression

A combination of numbers, operation signs, and sometimes letters or symbols that represents a value, such as 4 × n + 7. It becomes a single number once the unknown is replaced.

Long division steps

Repeat four steps: divide, multiply, subtract, and bring down the next digit. The remainder is always less than the divisor, so a remainder of 7 is impossible when dividing by 5.

Multi-digit multiplication

Multiply by each digit of the second factor, shifting one place left for each new digit, then add the partial products. Estimate first, as 38 × 412 is near 40 × 400 = 16,000.

Equivalent fractions

Fractions that name the same amount even though the numbers differ. Multiply or divide numerator and denominator by the same nonzero number: 3/4 = 9/12 = 0.75.

Simplest form

A fraction is in simplest form when the only common factor of numerator and denominator is 1. Divide both by their greatest common factor: 18/24 becomes 3/4.

Adding unlike fractions

Rewrite both fractions with a common denominator, add the numerators, and keep the denominator. 1/2 + 1/3 becomes 3/6 + 2/6 = 5/6.

Subtracting mixed numbers

Regroup one whole into a fraction when the top fraction is smaller. For 5 1/4 − 2 3/4, rename 5 1/4 as 4 5/4, then subtract to get 2 2/4, or 2 1/2.

Multiplying fractions

Multiply numerator by numerator and denominator by denominator, then simplify. 2/3 × 3/4 = 6/12 = 1/2; the product is smaller than either factor when both are below 1.

Multiplying mixed numbers

Change each mixed number to an improper fraction before multiplying. 1 1/2 × 2 2/3 becomes 3/2 × 8/3 = 24/6 = 4.

Dividing by unit fractions

Dividing by 1/n is the same as multiplying by n, because it asks how many 1/n pieces fit. 3 ÷ 1/4 = 12, a quotient larger than the starting number.

Fraction as scaling

Multiplying by a fraction greater than 1 makes the result larger, by a fraction less than 1 makes it smaller, and by exactly 1 leaves it unchanged. 20 × 3/4 = 15.

Fraction of a set

Multiply the fraction by the number of items to find the part. Three-fourths of 24 pencils is 3/4 × 24 = 18 pencils, found by dividing 24 by 4 and multiplying by 3.

Volume of rectangular prism

Volume equals length times width times height, or base area times height. A box 5 cm by 3 cm by 4 cm has volume 60 cubic centimeters.

Volume by unit cubes

Filling a solid with unit cubes and counting them gives its volume. A layer of 12 cubes stacked 3 layers high holds 36 cubes, so the volume is 36 cubic units.

Customary length units

Twelve inches make a foot, three feet make a yard, and 5,280 feet make a mile. To convert 4 yards to feet, multiply by 3 to get 12 feet.

Customary capacity units

Eight fluid ounces make a cup, two cups make a pint, two pints make a quart, and four quarts make a gallon. So one gallon equals 16 cups.

Metric conversions

Prefixes tell the size: kilo- is 1,000, centi- is 1/100, milli- is 1/1,000. So 2.5 meters equals 250 centimeters and 2,500 millimeters.

Metric mass and capacity

One kilogram equals 1,000 grams, and one liter equals 1,000 milliliters. A 750-milliliter bottle is 0.75 liter, less than one full liter.

Measurement word problems

Convert all quantities to the same unit before computing, then convert the answer back if asked. Adding 1 foot 6 inches to 10 inches requires changing feet to inches first.

Coordinate plane

Two perpendicular number lines cross at the origin, (0, 0). The first coordinate in an ordered pair gives horizontal distance and the second gives vertical distance.

Plotting ordered pairs

Start at the origin, move right or left by the x-coordinate, then up or down by the y-coordinate. For (4, 2), move 4 right and 2 up.

Graphing patterns

When two rules produce ordered pairs, plot both sets and compare. If every y-value of one rule is double the other, its points form a steeper line.

Line plot

A number line marked with X's above each value, one X per data item. The value with the tallest stack is the most common, and the spread shows the range.

Mean of a data set

Add all values and divide by how many there are. For 2, 4, 4, 6, the sum is 16 and the count is 4, so the mean is 4.

Unit fraction

A fraction with numerator 1, such as 1/2, 1/5, or 1/12. Every other fraction is a sum of unit fractions: 3/5 equals 1/5 + 1/5 + 1/5.

Mixed number to improper fraction

Multiply the whole number by the denominator, add the numerator, and place the total over the same denominator. 3 2/5 becomes 17/5.

Decimal to fraction

Read the decimal by its last place, then simplify. 0.75 is 75/100, which reduces to 3/4; 0.6 is 6/10, or 3/5.