Slice a pizza into four equal pieces. One slice of a pizza that has been sliced into fourths can be written using the fraction 1/4. The number on the bottom, the denominator, indicates how many equal pieces an object has been divided into. The number on the top, the numerator, indicates how many of those equal pieces you are working with.
Slice the second pizza into eight equal pieces. The fraction 1/8 indicates that you are working with one of eight equal pieces. Similarly, the fraction 3/8 would indicate that you are working with three of eight equal pieces.
Place a slice of the pizza that has been cut into fourths next to a slice of the pizza that has been cut into eighths. The slice that is equal to 1/4 of the pizza is bigger than the slice that is equal to 1/8 of a pizza. This example illustrates the fact that, when numerators are equal, larger denominators make the fraction smaller.
Place one slice of the pizza cut into fourths next to two slices of the pizza cut into eighths. Since the two amounts are the same, 1/4 and 2/8 are equivalent fractions because they use different numbers to express the same amount.
Place two slices of the pizza that has been cut into fourths next to four slices of the pizza that has been cut into eighths. The fractions 2/4 and 4/8 are also equivalent because the represent the same quantity of pizza.
Write the fractions 2/4 ad 4/8 next to each other.
Point to the numerator 2 in the fraction 2/4 and ask what number that 2 would have to be multiplied by to get it to equal the other numerator 4 in the fraction 4/8. In answering this question, it often helps to divide the larger numerator by the smaller one. In this case, divide 4 by 2 for an answer of 2. Therefore, the numerator of 2/4 would be multiplied by 2.
Point to the denominator 4 in the fraction 1/4 and ask what number to multiply by to get the denominator of 8 of the second fraction, 4/8. To find this answer, it often helps to divide the larger denominator, 8, by the smaller denominator, 4, for an answer of 2. Therefore, multiply the denominator, 4, by 2, for an answer of 8. When the numerator and denominator of a fraction are both multiplied by the same non-zero number (which can be any number, not necessarily 2) the answer is a new fraction that is equivalent to the original one.
Place a slice from the pizza cut in fourths next to a slice from the pizza cut into eighths. Think about how to express the total amount of pizza as one number.
Place two slices of the pizza cut into eighths next to one slice from the pizza cut into fourths. Looking at the slices shows that 2/8 is equivalent to 1/4. Therefore, instead of adding 1/4 + 1/8, you could add 2/8 + 1/8. To add fractions with the same denominator, add the numerators and keep the denominator for an answer of, in this case, 3/8.
Repeat the procedure above using one slice from the pizza cut into fourths and three slices from the pizza cut into eighths. Since one slice of the pizza cut into fourths is equivalent to two slices of pizza cut into eighths, the problem becomes 2/8 + 3/8 = 5/8. Remember to add the numerators and keep the denominator the same.
Place two slices of the pizza cut into fourths next to one slice cut into eighths. Ask if this amount is more than one-half of a pizza or less than one-half of a pizza. Obviously, this is more than one-half of a pizza.
Write down the expression 2/4 + 1/8. For the purposes of illustration, perform a mathematically incorrect action and add both numerator and denominator. The (wrong) answer is 3/12.
Slice the third pizza into twelfths and take three of those slices. Compare the amount of pizza in those three slices with the amount of pizza found by taking two slices of the pizza cut into fourths and one slice of the pizza cut into eighths. Since the two quantities are different, it is obvious that adding denominators will give the wrong answer.
Place one slice from the pizza that was cut into fourths next to two slices from the pizza that was cut into eighths.
Write the fractions representing the two amounts: 1/4 and 2/8. Because these two fractions represent the same amount of pizza, those two fractions are equivalent. Notice that 1/4 uses smaller numbers to represent that amount of pizza. The fraction with the smallest numbers that represents a given quantity is said to be in lowest terms.
Divide the numerator and denominator of a fraction by the largest number that divides evenly into both. This is called reducing to lowest terms. For example, to reduce 2/8 to lowest terms, divide both 2 and 8 by 2 for an answer of 1/4. This fraction, 1/4, is in lowest terms because the numerator cannot be divided any more.