Multiplying Fractions and Decimals

MULTIPLYING FRACTIONS AND DECIMAL NUMBERS The product of two numbers having the same sign is positive. The product of two numbers having different signs in negative. MULTIPLYING FRACTIONS AND DECIMAL NUMBERS Remember the following rules apply to fractions and decimals, as well as integers: 1) A positive times a positive is a positive. 2) A positive times a negative is a negative. 3) A negative times a negative is a positive.

EXAMPLE 1α: Find each product. a. (-9.8)4 b. Negative times positive yields negative. All that is left is to multiply 9.8 by 4 and put a negative sign on the result. (9.8)4 = 39.2 -39.2 Negative times negative yields a positive. Multiply the numbers. Reduce. Try it: Find each product. a. b. (-1.4)7

EXAMPLE 2α: Evaluate if a = 2. Plug 2 in for a. Exponent. Multiply. Multiply again. Reduce. Try it: Evaluate if a = 3.

MULTIPLICATIVE PROPERTY OF -1 The product of any number and -1 is its additive inverse. -1(a) = -a and a(-1) = -a MULTIPLICATIVE PROPERTY OF -1 Question: What is -1 times 5? Answer: -5 Question: What is -1 times -14? Answer: 14 Question: So what does multiplying by -1 do to any number? Answer: Multiplying by -1 changes only the sign of a number.

EXAMPLE 4α: Find Handle the first pair. We now have:

Try it: Multiply. a. b.

Dividing Fractions and Decimals

DIVIDING FRACTIONS AND DECIMAL NUMBERS The QUOTIENT of two numbers having the same sign is positive. The QUOTIENT of two numbers having different signs in negative. DIVIDING FRACTIONS AND DECIMAL NUMBERS Remember the following rules apply to fractions and decimals, as well as integers: 1) A positive divided by a positive is a positive. 2) A positive divided by a negative is a negative. 3) A negative divided by a negative is a positive.

Remember the dividing fractions algorithm!

The reciprocal of a number is called its multiplicative inverse. The reciprocal of is where a and b  0. The reciprocal of a number is called its multiplicative inverse. A number multiplied by its reciprocal/multiplicative inverse is ALWAYS equal to 1.

Example #1 The reciprocal of is Example #2 The reciprocal of -3 is

Basically, you are flipping the fraction! We will use the multiplicative inverses for dividing fractions.

Examples 1) When dividing fractions, change division to multiplying by the reciprocal.

2)

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When dividing a decimal by a decimal, multiply both numbers by a power of 10 so you can divide by a whole number. To decide which power of 10 to multiply by, look at the denominator. The number of decimal places is the number of zeros to write after the 1. 1.32 0.4 1.32 0.4 10 13.2 4 = = 1 decimal place 1 zero

Additional Example 2: Dividing Decimals Find 0.384 ÷ 0.24. 0.384 0.24 0.384 ÷ 0.24 = 100 38.4 24 = 38.4 24 = Divide. = 1.6

58.5 25 = Find 0.585 ÷ 0.25. Check It Out: Example 2 0.585 0.25 0.585 ÷ 0.25 = 100 Divide. = 2.34

Understand the Problem Additional Example 4: Problem Solving Application 1 2 A cookie recipe calls for cup of oats. You have cup of oats. How many batches of cookies can you bake using all of the oats you have? 3 4 Understand the Problem The number of batches of cookies you can bake is the number of batches using the oats that you have. List the important information: The amount of oats is cup. One batch of cookies calls for cup of oats. 12 34

, or 1 batches of the cookies. Make a Plan Set up an equation. Solve Let n = number of batches. 12 34 = n ÷ 21 • 64 , or 1 batches of the cookies.

Does my answer make sense? One cup of oats would make two batches so 1 is a reasonable answer. 12 You try it! A ship will use of its total fuel load for a typical round trip. If there is of a total fuel load on board now, how many complete trips can be made? 5 8 1 6 3 complete trips

Lesson Quiz Divide. 5 6 1 2 –1 89 1. ÷ –1 2. –14 ÷ 1.25 –11.2 3. 3.9 ÷ 0.65 6 112 x 4. Evaluate for x = 6.3 17.7 5. A penny weighs 2.5 grams. How many pennies would it take to equal one pound (453.6 grams)? about 181