Write and solve the addition or the subtraction expression that describes the given figure.
What do we see here? A blue portion and a green portion. Together, these two pieces create the total shaded part of the figure. The blue plus the green equals the total. We remember that a fraction is the part out of the whole.
This whole rectangle is made up of one, two, three, four, five, six, seven, eight, nine pieces. That means the base of our denominator is nine. Out of nine total pieces, only one of them is blue. The blue part is one-ninth.
Out of nine total pieces, the number of pieces that are shaded green is five. There are five green pieces. The green part is five-ninths. If we add one-ninth plus five-ninths, we add the numerator together one plus five equals six, and the denominator doesn’t change because we haven’t changed the number of pieces the rectangle is divided into.
The total shaded part is then six-ninths. When we look at six-ninths, we need to ask if we can reduce this value. Is there anything we can divide the numerator and the denominator by here? Both six and nine are divisible by three.
When we’re working with fractions, we can simplify our fractions if we divide the numerator and the denominator by the same value. Six divided by three is two. Nine divided by three is three. We can reduce six-ninths to two-thirds, and that means one- ninth plus five-ninths equals two-thirds.