Welcome to decimal and fraction multiplication! These two forms represent the same mathematical values. For example, 0.5 and one-half are identical. When we multiply 0.5 times 2, we get 1.0. Similarly, one-half times 2 equals 1. Today we'll learn systematic methods for multiplying both decimals and fractions, and discover when to use each approach.
Let's learn the systematic method for multiplying decimals. First, multiply the numbers as if they were whole numbers, ignoring the decimal points. Second, count the total number of decimal places in both original numbers. Third, place the decimal point in your answer so it has that many decimal places. For example, 0.3 times 0.2: multiply 3 times 2 equals 6, count decimal places one plus one equals two, so the result is 0.06. For larger numbers like 2.45 times 1.3: multiply 245 times 13 equals 3185, count decimal places two plus one equals three, giving us 3.185.
Now let's learn fraction multiplication. The rule is simple: multiply the numerators together and multiply the denominators together. For example, one-half times one-third equals one times one over two times three, which gives us one-sixth. For mixed numbers like two and one-fourth times one and one-third, first convert to improper fractions: nine-fourths times four-thirds. Then multiply: nine times four over four times three equals thirty-six over twelve, which simplifies to three. Visual models help us understand why this works by showing the overlapping areas.
Sometimes we need to convert between decimals and fractions for easier multiplication. To convert 0.25 to a fraction, write it as 25 over 100, then simplify to one-fourth. To convert two-thirds to a decimal, divide 2 by 3 to get approximately 0.667. Let's solve 0.25 times two-thirds using both methods. Method one: convert 0.25 to one-fourth, then multiply one-fourth times two-thirds equals two-twelfths, which simplifies to one-sixth. Method two: convert two-thirds to 0.667, then multiply 0.25 times 0.667 equals approximately 0.167. Both methods give equivalent results: one-sixth equals approximately 0.167.
Let's apply our skills to a real cooking problem. A recipe calls for 2.5 cups of flour, but you want to make only two-thirds of the recipe. How much flour do you need? We need to calculate 2.5 times two-thirds. Solution one: convert 2.5 to the fraction five-halves, then multiply five-halves times two-thirds equals ten-sixths, which simplifies to five-thirds or one and two-thirds cups. Solution two: convert two-thirds to 0.667, then multiply 2.5 times 0.667 equals approximately 1.667, which is about one and two-thirds cups. Both methods give the same answer: you need one and two-thirds cups of flour. Choose the method that feels most comfortable for each situation.