Download seventh grade you should know

SEVENTH GRADE “YOU SHOULD KNOW”
Study Guide and Practice
The Four Basic Operations:
1) Addition
**the SUM is the answer to an addition problem**
When adding whole numbers, be sure to line up the place values.
9545
+ 8982
18,527
When adding decimal numbers, be sure to line up the decimal
points and bring the decimal straight down into your answer.
4,785 + 9 + 2.307
4,785
9
+
2 .307
4,796.307
2) Subtraction
**the DIFFERENCE is the answer to a subtraction problem**
5,312
**Be sure to line up place value and borrow if need be**
− 2,579
2,733
When subtracting decimal numbers, you must line up the
decimal points, add zeros to match place value, subtract, and bring
decimal point straight down.
18.2 - 6.008 =
18.200
- 6.008
12.192
3) Multiplication
**the PRODUCT is the answer to a multiplication problem**
Multiply the top number by each place value of the bottom number
starting with the ones place. Remember to put a zero or indent
when multiplying by the next place value.
When multiplying with decimal numbers, the decimal points are
irrelevant until the very end. Multiply the numbers like normal and
count the number of digits that are behind the decimal point in
each number. This is how many places you move the decimal point
in the product beginning at the end of the number.
.2 × 6.03 = 1.206
***MENTAL MATH – when multiplying by 10 or 100 or 1000, keep
the original number and place 1, 2, or 3 zero at the end of the product.
36 × 10
= 360
36 × 100 = 3600
Add on one 0.
Add on two 0’s
36 × 1000 = 36,000 Add on three 0’s
7.32 × 10 = 73.2 Move the decimal point one place right.
4) Division
**the QUOTIENT is the answer to a division problem**
**the DIVIDEND is the number that is inside the division box**
**the DIVISOR is the number that is outside the division box**
** If there is a remainder, we no longer use the “R.” All remainders
must be expressed as a decimal or fraction.**
When dividing with decimals: if there is a decimal point in the
divisor, you must move that decimal to the end of the number and
then move the decimal point the same number of places in the
dividend. Divide like normal and move the decimal point straight up
in your quotient.
***MENTAL MATH: when dividing by 10 or 100 or 1000, move the
decimal in to the left.
256 ÷ 10 = 25.6
256 ÷ 100 = 2.56
256 ÷ 1000 = .256
move the decimal 1 place
move the decimal in 2 places
move the decimal point in 3 places
Practice: On your Own
1) 697 + 341 =
7) 56.3 – 8.987 =
2) 1, 234 + 876 =
8) 5.1 × 3.7 =
3) 34.987 + 5.9 =
9) 12 × 56 =
10)
1.21 × .05 =
4) 87.3 + 4.234 + 9 =
11) 804 ÷ 3 =
5) 93.32 – 9.3 =
6) 127 – 99 =
12)
1245 ÷ 27 =
13)
56.2 ÷ .02 =
PLACE VALUE:
COMPARING AND ORDERING:
SYMBOLS:
< less than
> greater than
= equal
***When we compare and order whole numbers and/or decimal
numbers, we compare place value to place value***
14,987 > 14, 912
the 8 is greater than the 1 in the tens place
5,123.6 < 5,124
the 3 is less than the 4 in the ones place
9.00876 < 9.09
the 0 is less than the 9 in the hundredths place
5.6 = 5.600
the zeros at the end of a decimal number do not
affect the number
Writing Numbers
1) Standard Numerical Form – written as a number
ex: ninety-four thousand, sixty-two 94,062
2) Written word form – take a number and write it using
words, dashes, and commas
ex: 153.097 one hundred fifty-three and ninetyseven thousandths
3) Expanded Form – separate the number into the sum of each
place value
ex: 91,045.2
90,000 + 1000 + 40 + 5 + .2
Estimating and Rounding
Estimate – a close guess (round before performing the
operation)
923 + 490 + 313 ≈ 900 + 500 + 300 ≈ 1700
Rounding
- look to the number to the right of the given place value
- 5 and above, round up
- Less than 5, round down
78,987 round to the thousand : 79,000
34,244 round to the hundred: 34,200
125.245 round to the hundredths : 125.25
67,998 round to the hundred : 68,000
Practice: On your Own!!
1) Identify the place value of the 9 in each of the following number:
1) 45,921 ___________________
2) 8.987 ____________________
3) 62.009 ___________________
4) 9,000,000 ________________
2) Compare using < , >, or =
5)
9.87
8.976
6)
41.9776
41.862
7)
56.213
5.613
8)
9.003
9.0030
3)
Round 45,234 to the tens ________________
4)
Round 38,762.355 to the hundredths ____________
5)
Estimate the sum of 346 + 2345 + 467 = ______________
6)
Write 943.96 in written and expanded form.
Written ___________________________________
Expanded __________________________________
Divisibility Rules:
Divisible – can be divided by
We know that a number is divisible by:
2: when the ones digit is even (346)
3: when the sum of the digits is divisible by 3 (123)
4: when the last two digits is divisible by 4 (336)
5: when the ones digit is a 5 or 0 (900)
6: when the number is divisible by 2 and 3
(246)
8: when the last three digits are divisible by 8 (4720)
9: when the sum of the digits is divisible by 9 (279)
10: when the ones digit is a 0 (450)
Prime: a number that has only two factors; one and itself
examples: 2, 3, 5, 7, 11, 13…
Factor: numbers that can divide evenly
into a larger number.
(without a remainder)
**smallest (and only even) prime number = 2
Composite: a number that has more than 2 factors
examples: 4, 6, 8, 9, 10…
***ONE and ZERO are neither prime nor composite!!
Prime Factorization: the breakdown of a composite number
into the product of all of its prime
factors.
Example:
Practice: On your Own
Use the divisibility rules to determine which numbers the following are divisible by:
1) 456 ___________________________________
2) 200 ___________________________________
3) 135____________________________________
4) 117____________________________________
Tell whether the following numbers are prime, composite, or neither:
5) 16 __________
6) 81 _________
7) 97 __________
8) 1 __________
9) 91 ___________
10) 30 __________
Determine the Prime Factorization of each number:
11) 72
12) 156
GREATEST COMMON FACTOR (GCF): the largest factor that two
or more numbers have in common
LEAST COMMON MULTIPLE (LCM):the smallest multiple that two
or more numbers have in common
MULTIPLE – the product of a number with any whole number
Practice: On your Own
Determine the GREATEST COMMON FACTOR of each set of numbers:
1) 30, 48
2) 100, 25
Determine the LEAST COMMON MULTIPLE of each set of numbers:
3) 30, 45
4) 50, 75
Exponents:
The Exponent of a number shows how many times that number is to
be used in a multiplication problem. The Exponent is written as a
small number to the right and above the base number.
Squared – a number to the second power
Cubed – a number to the third power
Square Roots:
The square root of a number is a value that, when multiplied by
itself, gives the number.
Practice: On your Own
Evaluate:
1) 43 =
2) 24 =
3) 32 + 42 =
4) 102 – 82 =
5)
144 =
6)
900 =
7)
225 =
8)
196 =
9) 53 - 64 =
10) 23 × 100 =