Math: Fractions and Decimals 111
What is a decimal? A decimal is a type of fraction in which:
The denominator is a power of ten.
Precision
The dispersion of measurements or fineness of readings. More decimals in measurements indicate a need for higher precision.
Greatest Common Factor
The highest number that can evenly divide into two numbers. Finding the greatest common factor of the numerator and the denominator is the first step to reducing a fraction.
Denominator
The number on the bottom of a fraction. The denominator expresses the quantity of total parts into which the whole number has been divided.
Numerator
The number on the top of a fraction. The numerator indicates the number of parts of the whole.
Place Value
The numerical value of a digit, based on its position in the number. Place value is expressed in groups of ten.
Decimal Point
The period between whole numbers and decimals. The higher the number of places to the right of the decimal point, the smaller the decimal's value.
Divisor
The quantity by which a number is divided. The divisor is in the denominator of a fraction.
Dividend
The quantity that a number is divided into. The dividend is in the numerator of a fraction.
Lowest Common Denominator
The smallest possible denominator that can be shared by two fractions. The lowest common denominator is used when adding or subtracting fractions with different denominators.
Invert
To switch the locations of the numerator and denominator. Invert the second fraction when dividing with fractions, and then multiply.
Borrow
To take an amount from the whole number in a mixed number and add it to the fraction. Borrowing changes the way the number is expressed but does not change its value.
Operation
A mathematical action or process such as addition or subtraction. A mathematical equation can consist of multiple operations.
Rounding
A method used to shorten numbers. Rounding involves either increasing or decreasing a number to the next digit.
Factor
A number that evenly divides another number. For example, 3 is a factor of 12 because 12 can be divided by 3 with no remainder (12/3=4).
Percentages
A number that indicates part of a whole. Percentages are fractions in which the denominator is 100.
Fraction
A number that indicates parts of a whole number. Fractions appear as one number over the other with a slash or horizontal line between them.
Decimal
A type of fraction in which the denominator is always a power of ten and the numerator is indicated by values placed to the right of a decimal point. Decimals include 2.7, 0.41, and so on.
Mixed Number
A whole number combined with a fraction. Mixed numbers can be converted to improper fractions, and improper fractions can be converted to mixed numbers.
Which of the following terms is used to describe a fraction that has a numerator that is larger than the denominator?
Improper fraction
Which of the following steps must be performed first to round the decimal 0.135 to the hundredths place?
Increase the digit in the hundredths place by one.
Which of the following terms describes a fraction that is combined with a whole number?
Mixed number
Which of the following actions converts a percentage to a decimal?
Moving the decimal point two places to the left.
Which of the following actions converts a decimal to a percentage?
Moving the decimal two places to the right.
What is the first step to convert 9 3/8 from a mixed number to an improper fraction?
Multiply 9 by 8.
Which statement about fractions is true? Fractions appear as:
One number over another, separated by a line.
Remainder
When dividing one number into another, any left over amount that does not divide into the numerator. When converting improper fractions, remainders become the numerator of the fraction in the mixed number.
An item that normally costs $56.00 is reduced by 25%. How much will the item cost after the reduction?
$42.00
What is 7% of 204?
14.28
Convert the mixed number 5 3/16 to an improper fraction.
83/16
0.0649 rounded to the nearest hundredth equals:
0.06
Solve the sample problem. 4.13 x 0.017
0.07021
Find the answer to the problem 0.1249 + 0.037.
0.1619
0.68 - 0.287 =
0.393
A bar with a diameter of 0.75 inches needs to be reduced by 40%. What will the new diameter of the bar be?
0.45 inches
Solve the sample problem. 2.17 x 0.28
0.6076
Solve the sample problem. 0.0532 + 0.71
0.7632
Find the answer to the sample problem. Reduce the answer to its lowest terms. 4 1/2 ÷ 2 2/3
1 11/16
A 12 inch bar needs to have 10% trimmed off of one end. How much will be cut off of the bar?
1.20 inches
Find the answer to the sample problem. Reduce the answer to its lowest terms. 3/7 x 21/72
1/8
Find the answer to the problem 2 1/3 x 4 1/2 Reduce the answer to its lowest terms.
10 1/2
Find the answer to the sample problem. Reduce the answer to its lowest terms. 14 5/32 - 3 10/32
10 27/32
8.64 ÷ .8 =
10.8
Find the answer to the sample problem. Reduce the answer to its lowest terms. 7 3/12 + 4 2/3
11 11/12
Find the answer to the problem 2 3/6 + 9 1/3. Reduce the answer to its lowest terms.
11 5/6
Solve the sample problem. 4.75 ÷ 0.43
11.05
Solve the sample problem. 16 - 3.211
12.789
Which of these statements concerning percents is true? A percentage is a fraction with:
A denominator of 100.
Common Factor
A factor that is shared by two or more numbers. For example, 4 is a common factor of 8 and 12 because 4 divides 8 and 12 evenly (8/4=2, 12/4=3).
Find the answer to the sample problem. Reduce the answer to its lowest terms. 7 1/5 x 2 1/4
16 1/5
Find the answer to the sample problem. Reduce the answer to its lowest terms. 31/35 - 6/14
16/35
Find the answer to the sample problem. Reduce the answer to its lowest terms. 32/24 ÷ 5/12
16/5
Find the answer to the problem 10 4/8 - 7 3/4. Reduce the answer to its lowest terms.
2 3/4
Convert the improper fraction 21/8 to a mixed number.
2 5/8
Solve the problem 2.741 - 0.568.
2.173
6/14 - 1/7 =
2/7
7/10 ÷ 2/3 =
21/20
8 ¾ x 2 5/8=
22 31/32
Find the answer to the sample problem. Reduce the answer to its lowest terms. 5/6 + 1/8
23/24
Find the answer to the problem 6 3/4 ÷ 2 1/6. Reduce the answer to its lowest terms.
3 3/26
1.59 x 4.15 =
6.5985
3/4 x 4/7 =
3/7
Solve the sample problem. 5.13 ÷ 0.017
301.76
Find the answer to the sample problem. Reduce the answer to its lowest terms. 3/10 + 5/8
37/40
3 4/9 ÷ 7 ½ =
62/135
1.456 + 6.02 =
7.476
Find the answer to the sample problem. Reduce the answer to its lowest terms. 7/16 x 4/9
7/36
4 1/2 + 3 7/8 =
8 3/8
What is 13% of 363?
47.19
1/4 + 3/8 =
5/8
Find the answer to the sample problem. Reduce the answer to its lowest terms. 39/40 - 7/20
5/8
Improper Fraction
A fraction in which the numerator is larger than the denominator. Improper fractions equal amounts greater than one.
Whole Number
Any number that has not been divided into fractions or decimals. Whole numbers include 1, 2, 3, 10, 15, 23, and so on.
What is the first step to convert 22/3 from an improper fraction to a mixed number?
Divide 22 by 3.
What is the first step to converting from a fraction to a decimal?
Divide the numerator by the denominator.
Which of the following steps is required to round the decimal 1.2431 to the tenths place?
Drop every digit to the right of the tenths place.
To reduce a fraction, what value should be found first?
Greatest common factor
Proportional
Having a constant amount in relation to another quantity. For two numbers to be proportional, as one number increases, the other should increase by an equal factor.
Which of the following statements describes the denominator of a fraction? The denominator is a number that indicates:
How many total parts into which the whole has been divided.
Which of the following is a way to express a certain portion of 100?
Percentage
Finding the greatest common factor of a fraction's numerator and denominator is the first step for which of the following?
Reducing a fraction.
Which statement about fractions is true? Fractions:
Represent parts of a whole quantity.