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In a cookbook, a picture of a cake is printed to a scale of 1:4. The cake measures 5 cm in the picture. How large is it in reality?
Maria works extra time at the stables. She wants to put up a sign with a horse on it so that people passing by could see that this is a stable. She made a sketch of the stable which she rolls out onto the table. "Here is where the sign will be," Maria thinks, "and it should look like this. This is big enough." Now she only has to make the sign. On the sketch the sign is 20 cm wide.
How big is it in reality? When Maria made this sketch she measured the stable carefully. Maria represented every meter in reality as one decimeter, or one tenth of a meter on the sketch. Look at the corner of the sketch. There it says scale 1:10.
The first number means the distance in the sketch. The second one means the distance in reality. The colon in the middle works just like a fraction bar. Scale one to ten therefore, means that the sketch is one tenth of the real size. But when we deal with a scale, we use a colon instead of a fraction bar.
And we read the colon as to. In this sketch one centimeter corresponds to ten centimeters in reality. When Maria makes the sign she wants it to be the right size so it's an accurate representation of the sketch. She wants to make it according to the scale. 20 centimeters in the sketch. 10 times bigger in reality.
20 times 10, the sign should be 200 centimeters wide which is 2 meters. There we go. That's nice, isn't it? Maria is doing a presentation on how to shoe a horse, and she wants to bring a poster with her. She has a picture of a horseshoe which she wants to show. The real horseshoe is 15 centimeters long.
But for the whole class to see properly she wants to make the picture five times as big. In other words 75 centimeters. The scale is therefore, five to one. Five centimeters in the picture represent one centimeter in reality. Since the first number is larger than the second one it's an enlargement.
There we go. A horseshoe according to the scale where every measurement is five times bigger in the picture than it is in reality. The scale shows the ratio between a distance in reality, and a corresponding distance in a picture. The scale is expressed in the form of a fraction, but with a colon instead of a fraction bar. The colon is read as to.
The scale shows the distance between two points in the picture divided by the actual distance between them. If the first number from the picture is larger it's an enlargement. If the second number, the actual size, is larger it's a reduction. If the scale is one to one the sketch is made in actual size.